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Embedded unbounded order convergent sequences in topologically convergent nets in vector lattices Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-03-12 Yang Deng, Marcel de Jeu
We show that, for a class of locally solid topologies on vector lattices, a topologically convergent net has an embedded sequence that is unbounded order convergent to the same limit. Our result implies, and often improves, many of the known results in this vein in the literature. A study of metrisability and submetrisability of locally solid topologies on vector lattices is included.
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The skew commutators of Toeplitz operators or Hankel operators on Hardy spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-03-06 Yongning Li, Hanyi Zheng, Xuanhao Ding
Let A and B be two bounded linear operators on a Hilbert space. B is called the skew commutator of A if \(_{*}[A, B]=AB-BA^{*}=0.\) In this paper, we completely characterize when a Toeplitz operator on the Hardy space is a skew commutator of a Hankel operator and when a Hankel operator on the Hardy space is a skew commutator of a Toeplitz operator. Moreover, we also obtain a necessary and sufficient
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Carleson measures and Berezin-type operators on Fock spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-03-04 Lifang Zhou, Dong Zhao, Xiaomin Tang
We characterize (vanishing) Fock–Carleson measures by products of functions in Fock spaces. We also study the boundedness of Berezin-type operators from a weighted Fock space to a Lebesgue space. Due to the special properties of Fock–Carleson measures, the boundedness of Berezin-type operators on Fock spaces is different from the corresponding results on Bergman spaces.
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An existence result for a suspension of rigid magnetizable particles Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-03-02 Grigor Nika, Bogdan Vernescu
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Sharp embedding between Wiener amalgam and some classical spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-02-29
Abstract This paper investigates the embedding relationships between Wiener amalgam spaces and classical spaces, including Sobolev spaces, local Hardy spaces, Besov spaces, and \(\alpha \) -modulation spaces. By establishing exact conditions, we provide a detailed characterization of the embeddings between Wiener amalgam spaces and these classical spaces, particularly the most general case when \(\alpha
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Banach–Stone theorems for disjointness preserving relations Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-02-29 Denny H. Leung, Wee Kee Tang
The concept of disjointness preserving mappings has proved to be a useful unifying idea in the study of Banach–Stone type theorems. In this paper, we examine disjointness preserving relations between sets of continuous functions (valued in general topological spaces). Under very mild assumptions, it is shown that a disjointness preserving relation is completely determined by a Boolean isomorphism between
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Commutators for certain fractional type operators on weighted spaces and Orlicz–Morrey spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-02-28
Abstract In this paper, we focus on a class of fractional type integral operators that can be served as extensions of Riesz potential with kernels $$\begin{aligned} K(x,y)=\frac{\Omega _1(x-A_1 y)}{|x-A_1 y |^{{n}/{q_1}}} \cdots \frac{\Omega _m(x-A_m y)}{|x-A_m y |^{{n}/{q_m}}}, \end{aligned}$$ where \(\alpha \in [0,n)\) , \( m\geqslant 1\) , \(\sum \limits _{i=1}^m\frac{n}{q_i}=n-\alpha \) , \(\{A_i\}^m_{i=1}\)
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Non-smooth atomic decomposition of Triebel–Lizorkin-type spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-02-22 Yoshihiro Sawano, Dachun Yang, Wen Yuan
In this article, the authors establish a non-smooth atomic decomposition of Triebel–Lizorkin-type spaces and, as a by-product, a non-smooth atomic decomposition of subspaces of BMO spaces is obtained. An application of this decomposition method to the boundedness of Marcinkiewicz integral operators is also presented.
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Greedy-like bases for sequences with gaps Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-02-21 Miguel Berasategui, Pablo M. Berná
In 2018, Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the \({{\textbf {n}}}\)-t-quasi-greedy property that is based on them. Building upon this foundation, our current work aims to further investigate these algorithms and bases while introducing new ideas for two primary purposes. First, we aim to prove that for \({{\textbf
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Limiting dynamics for stochastic delay p-Laplacian equation on unbounded thin domains Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-02-18 Fuzhi Li, Dingshi Li, Mirelson M. Freitas
We study the long-term behavior of solutions for stochastic delay p-Laplacian equation with multiplicative noise on unbounded thin domains. We first prove the existence and uniqueness of tempered random attractors for these equations defined on \((n+1)\)-dimensional unbounded thin domains. Then, the upper semicontinuity of these attractors when a family of \((n+1)\)-dimensional thin domains degenerates
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The solvability of inhomogeneous boundary-value problems in Sobolev spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-02-17 Vladimir Mikhailets, Olena Atlasiuk
The aim of the paper is to develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of arbitrary order in Sobolev spaces. Boundary conditions are allowed to be overdetermined or underdetermined. They may contain derivatives, of the unknown vector-valued function, whose integer or fractional orders exceed the order of the
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Characterizations of generalized pencils of pairs of projections Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-02-12 Tao Chen, Weining Lai, Chunyuan Deng
Let T be a bounded linear operator on a complex Hilbert space \(\mathcal {H}\). We present some necessary and sufficient conditions for T to be the generalized pencil \(P + \alpha Q +\beta PQ\) of a pair (P, Q) of projections at some point \((\alpha , \beta )\in \mathbb {C}^2\). The range and kernel relations of the generalized pencil T are studied and comments on the additional properties of some
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Sharp norm estimates for functional dual affine quermassintegrals Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-01-28 Songjun Lv
This paper presents refined estimates for functional dual affine quermassintegrals, building upon the estimates of Dann et al. To sharpen the inequality, Dann et al. (Proc. Lond. Math. Soc. (3) 113(2):140–162, 2016) incorporated an \(L^\infty\)-weight into the integration. We further refine these estimates and extend the \(L^\infty\)-weight estimates to include a wider range of \(L^{\lambda }\)-weights
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p-Summing Bloch mappings on the complex unit disc Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-01-22 M. G. Cabrera-Padilla, A. Jiménez-Vargas, D. Ruiz-Casternado
The notion of p-summing Bloch mapping from the complex unit open disc \(\mathbb {D}\) into a complex Banach space X is introduced for any \(1\le p\le \infty .\) It is shown that the linear space of such mappings, equipped with a natural seminorm \(\pi ^{\mathcal {B}}_p,\) is Möbius-invariant. Moreover, its subspace consisting of all those mappings which preserve the zero is an injective Banach ideal
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Boundedness of maximal function for weighted Choquet integrals Banach J. Math. Anal. (IF 1.2) Pub Date : 2024-01-16 Keng Hao Ooi
We study the boundedness of Hardy–Littlewood maximal function on the spaces defined in terms of Choquet integrals associated with weighted Bessel and Riesz capacities. As a consequence, we obtain a class of weighted Sobolev inequalities.
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On the reflexivity properties of Banach bundles and Banach modules Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-12-15 Milica Lučić, Enrico Pasqualetto, Ivana Vojnović
In this paper, we investigate some reflexivity-type properties of separable measurable Banach bundles over a \(\sigma \)-finite measure space. Our two main results are the following: The fibers of a bundle are uniformly convex (with a common modulus of convexity) if and only if the space of its \(L^p\)-sections is uniformly convex for every \(p\in (1,\infty )\). The fibers of a bundle are reflexive
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Compact linear combinations of composition operators on Hilbert spaces of Dirichlet series Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-12-05 Maofa Wang, Zhongbing Xie
We study linear combinations of two composition operators induced by linear symbols on the Hilbert space of Dirichlet series. Based on partial reproducing kernels, we obtain an equivalent inscription of the compactness of a single composition operator and describe the compact linear combinations of composition operators.
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Transfer operators and conditional expectations: the non-commutative case, the case of mu-Brownian motions and white noise space setting Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-11-21 Daniel Alpay, Palle Jorgensen
Our focus is the operators of multivariable stochastic calculus, i.e., systems of transfer operators, covariance operators, conditional expectations, stochastic integrals, and the counterpart infinite-dimensional stochastic derivatives. In this paper, we present a new operator algebraic framework which serves to unify the analysis and the interrelations for the operators in question. Our approach uses
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Universal composition operators on weighted Dirichlet spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-11-16 Kaikai Han, Yanyan Tang
It is known that the invariant subspace problem for Hilbert spaces is equivalent to the statement that all minimal non-trivial invariant subspaces for a universal operator are one dimensional. In this paper, we first give a characterization of the boundedness of composition operators on weighted Dirichlet spaces \({\mathcal {D}}_{\alpha }(\Pi ^{+})\) over the upper half-plane \(\Pi ^{+}\) using generalized
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Phase retrieval from intensity difference of linear canonical transform Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-11-02 Youfa Li, Guangde Wu, Yanfen Huang, Ganji Huang
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Orthogonalization in Clifford Hilbert modules and applications Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-10-31 Jinxun Wang, Tao Qian
We prove that the Gram–Schmidt orthogonalization process can be carried out in Hilbert modules over Clifford algebras, in spite of the un-invertibility and the un-commutativity of general Clifford numbers. Then, we give two crucial applications of the orthogonalization method. One is to give a constructive proof of existence of an orthonormal basis of the inner spherical monogenics of order k for each
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Iterative kernel density estimation from noisy-dependent observations Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-10-30 Yaxu Li
We consider the nonparametric estimation of the density function of an underlying random variable from a sequence of strongly mixing noisy observations. We develop a two-step estimation procedure to accomplish this task. At the first step, we propose an appropriate nonparametric kernel density estimation based on the observations, which allows a flexible bandwidth matrix. At the second step, we invoke
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Harmonic and polyanalytic functional calculi on the S-spectrum for unbounded operators Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-10-13 Fabrizio Colombo, Antonino De Martino, Stefano Pinton
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Topological aspects of quasi *-algebras with sufficiently many *-representations Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-10-09 Giorgia Bellomonte, Camillo Trapani
Quasi *-algebras possessing a sufficient family \(\mathcal {M}\) of invariant positive sesquilinear forms carry several topologies related to \(\mathcal {M}\) which make every *-representation continuous. This leads to define the class of locally convex quasi GA*-algebras whose main feature consists in the fact that the family of their bounded elements, with respect to the family \(\mathcal {M}\),
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Classification of doubly $${{\mathcal {U}}}$$ -commuting row isometries Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-10-10 Gelu Popescu
In this paper, we study the structure of the k-tuples of doubly \({{\mathcal {U}}}\)-commuting row isometries and the \(C^*\)-algebras they generate, where \({{\mathcal {U}}}\) is a set of commuting unitary operators on a Hilbert space. We obtain Wold decompositions and use them to classify the k-tuples of doubly \({{\mathcal {U}}}\)-commuting row isometries up to a unitary equivalence. We prove that
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Mean random attractors of stochastic lattice fractional delay Gray–Scott equations in higher moment product sequence spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-10-10 Xiaolan Qin, Lianbing She, Renhai Wang
This paper is devoted to the study of mean attractors in some higher moment product sequence spaces for a three-component reversible lattice stochastic Gray–Scott equation, where the nonlinear terms have polynomial growth of arbitrary orders, and the diffusion term is a locally Lipschitz function with a time-delay effect. We first formulate the equation into an abstract one in \(\mathbb {L}^2=:\ell
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Characterizations on upper semi-Fredholmness of two-by-two operator matrices Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-10-03 Lili Yang, Xiaohong Cao
Suppose that \({{\mathcal {H}}}\) and \({{\mathcal {K}}}\) are infinite dimensional separable Hilbert spaces. We denote by \(M_C=\left( \begin{array}{cc} A &{} C \\ 0 &{} B \\ \end{array} \right) \) the \(2\times 2\) operator matrix acting on \(\mathcal {H\oplus K},\) where \(A\in {\mathcal {B}}({\mathcal {H}}),\) \(B\in {\mathcal {B}}({\mathcal {K}})\) and \(C\in {\mathcal {B}}({\mathcal {K}}, {\mathcal
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Linear preservers of m-selfadjoint operators and high-order isometries Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-10-02 Hakima Mohsine, Zouheir Amara, Mourad Oudghiri
Let H be a complex infinite-dimensional Hilbert space. Given a positive integer m, a bounded linear operator T on H is called m-selfadjoint if \(\sum _{k=0}^m(-1)^{k}\left( {\begin{array}{c}m\\ k\end{array}}\right) T^{*m-k} T^{k}=0\), and is called m-isometry if \(\sum _{k=0}^m(-1)^{m-k} \left( {\begin{array}{c}m\\ k\end{array}}\right) T^{*k} T^{k}=0\). In the present paper, we focus on linear maps
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Asymptotical behavior of non-autonomous stochastic reaction–diffusion equations with variable delay on $${\mathbb {R}}^N$$ Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-09-25 Wenqiang Zhao, Zhi Li
In this paper, we study the asymptotical behavior of solutions of stochastic reaction–diffusion equations with a super non-linearity and a Lipschizt continuous variable delayed term. The existence and uniqueness of tempered measurable pullback attractors are established in \(C([-\hbar ,0];H^1({\mathbb {R}}^N))\). On account of the unobtainable bound of solution in \(H^2({\mathbb {R}}^N)\) caused by
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Characterizations of matrix-valued asymmetric truncated Hankel operators Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-09-26 Rewayat Khan, Ji Eun Lee
In this paper, we introduce the class of matrix-valued asymmetric truncated Hankel operators. By using characterizations of matrix-valued asymmetric truncated Toeplitz operators, we characterize matrix-valued asymmetric truncated Hankel operators in the case when two involved inner matrices are J-symmetric.
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Some new restricted maximal operators of Fejér means of Walsh–Fourier series Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-09-12 Davit Baramidze, Lasha Baramidze, Lars-Erik Perssson, George Tephnadze
In this paper, we derive the maximal subspace of natural numbers \(\left\{ n_{k}:k\ge 0\right\} ,\) such that the restricted maximal operator, defined by \({\sup }_{k\in {\mathbb {N}}}\left| \sigma _{n_{k}}F\right| \) on this subspace of Fejér means of Walsh–Fourier series is bounded from the martingale Hardy space \(H_{1/2}\) to the Lebesgue space \(L_{1/2}.\) The sharpness of this result is also
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Bounded below composition operators on the space of Bloch functions on the unit ball of a Hilbert space Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-09-04 Alejandro Miralles
Let \(B_E\) be the open unit ball of a complex finite or infinite dimensional Hilbert space E and consider the space \(\mathcal {B}(B_E)\) of Bloch functions on \(B_E\). Using Lipschitz continuity of the dilation map on \(B_E\) given by \(x \mapsto (1-\Vert x\Vert ^2) \mathcal {R}f(x)\) for \(x \in B_E\), where \(\mathcal {R}f\) denotes the radial derivative of \(f \in \mathcal {B}(B_E)\), we study
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A Markovian and Roe-algebraic approach to asymptotic expansion in measure Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-09-04 Kang Li, Federico Vigolo, Jiawen Zhang
In this paper, we conduct further studies on geometric and analytic properties of asymptotic expansion in measure. More precisely, we develop a machinery of Markov expansion and obtain an associated structure theorem for asymptotically expanding actions. Based on this, we establish an analytic characterisation for asymptotic expansion in terms of the Druţu–Nowak projection and the Roe algebra of the
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Reflexivity of finite-dimensional sets of operators Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-09-01 Janko Bračič
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Generalization of the HSIC and distance covariance using PDI kernels Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-08-29 Jean Carlo Guella
Hilbert–Schmidt independence criterion and distance covariance are methods to describe independence of random variables using either the Kronecker product of positive definite kernels or the Kronecker product of conditionally negative definite kernels. In this paper we generalize both methods by providing an independence criteria using a new concept, of positive definite independent kernels. We provide
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Approximation of kernel projection operators in shift-invariant subspaces of function spaces with mixed norms Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-08-29 Junjian Zhao, Guangwei Qu, Wei-Shih Du, Yasong Chen
In this paper, we study the approximation problems of the kernel projection operators with mixed norms. Moreover, we give the approximation order for this kind of projection operators. Our new results on approximation based on mixed norms are the extension of the traditional conclusions, but our research techniques are original and different from the traditional methods because of the non-commutativity
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Variable-coefficient viscoelastic wave equation with acoustic boundary conditions: global existence, blowup and energy decay rates Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-08-15 Jiali Yu, Huafei Di
This paper deals with the following initial acoustic boundary value problem for a variable-coefficient wave equation with memory term $$\begin{aligned}{} & {} u_{tt}-\Delta u-\Delta u_{t}-\Delta u_{tt}+\int _{0}^{t}b(t-s){\textrm{div}} (a_{1}(x)\nabla u(s)){\textrm{d}}s\\{} & {} \quad +\,a_{2}(x)u_{t}|u_{t}|^{q-2}=u|u|^{p-2}. \end{aligned}$$ Firstly, we get the global existence of solutions by energy
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On symmetric points with respect to the numerical radius norm Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-08-09 Souvik Ghosh, Arpita Mal, Kallol Paul, Debmalya Sain
We study left symmetric and right symmetric points with respect to the numerical radius orthogonality (respectively, known as nr-left symmetric operators and nr-right symmetric operators) in the setting of both Hilbert spaces and Banach spaces. We prove that a bounded linear operator T on a complex Hilbert space is nr-left symmetric if and only if T is the zero operator, provided that T attains its
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Rates of convergence for Jakimovski–Leviatan operators in terms of the Ditzian–Totik modulus Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-07-31 Ana-Maria Acu, José A. Adell, Ioan Raşa
We obtain uniform convergence results for the Jakimovski–Leviatan operators \(\Psi _n\) in terms of the Ditzian–Totik modulus, providing at the same time explicit upper constants. A main ingredient of the proof is the representation of such operators as an infinite linear combination of Szász–Mirakyan operators. Closed-form expressions for the moments of \(\Psi _n\) involving the Touchard polynomials
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Tingley’s problem for complex Banach spaces which do not satisfy the Hausdorff distance condition Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-07-28 David Cabezas, María Cueto-Avellaneda, Yuta Enami, Takeshi Miura, Antonio M. Peralta
In 2022, Hatori gave a sufficient condition for complex Banach spaces to have the complex Mazur–Ulam property. In this paper, we introduce a class of complex Banach spaces B that do not satisfy the condition but enjoy the property that every surjective isometry on the unit sphere of such B admits an extension to a surjective real linear isometry on the whole space B. Typical examples of Banach spaces
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Quaternionic Gabor frame characterization and the density theorem Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-07-21 Xiao-Li Zhang, Yun-Zhang Li
The study of quaternionic Gabor systems has interested some mathematicians in recent years. From the literature, we found that most existing results on quaternionic Gabor frames focus on the case of the product of time-frequency shift parameters being equal to 1, and have a gap that the involved quaternionic Gabor systems are all incomplete according to the symmetric real scalar inner product. In this
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Endpoint Sobolev regularity of higher order maximal commutators Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-07-21 Feng Liu, Yuan Ma
This paper is devoted to presenting some \(W^{1,1}\)-regularity properties of higher order maximal commutator and its fractional variant. More precisely, let \(k\ge 1,\) \(\alpha \in [0,1)\) and \(b\in L_{\textrm{loc}}^1 ({\mathbb {R}})\). We consider the following k-th order fractional maximal commutator $$\begin{aligned} {\mathfrak {M}}_{b,\alpha }^kf(x)=\sup \limits _{t>0}(2t)^{\alpha -1}\int _
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Completeness of exponentials and Beurling’s theorem on $$\mathbb R^n$$ and $$\mathbb T^n$$ Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-07-14 Santanu Debnath, Suparna Sen
A classical result of Arne Beurling states that the Fourier transform of a non-zero complex Borel measure \(\mu \) on the real line cannot vanish on a set of positive Lebesgue measure if \(\mu \) has certain decay. We prove a several variable analogue of Beurling’s theorem by exploring its connection with the well-known problem concerning the density of linear span of exponentials in a certain weighted
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Flat portions of the numerical range of a $$6 \times 6$$ companion matrix Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-07-14 Swastika Saha Mondal, Sarita Ojha, Riddhick Birbonshi
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Duality for $$\alpha $$ -Möbius invariant Besov spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-07-12 Guanlong Bao, Zengjian Lou, Xiaojing Zhou
For \(1\le p\le \infty \) and \(\alpha >0\), Besov spaces \(B^p_\alpha \) play a key role in the theory of \(\alpha \)-Möbius invariant function spaces. In some sense, \(B^1_\alpha \) is the minimal \(\alpha \)-Möbius invariant function space, \(B^2_\alpha \) is the unique \(\alpha \)-Möbius invariant Hilbert space, and \(B^\infty _\alpha \) is the maximal \(\alpha \)-Möbius invariant function space
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Localization operators on discrete modulation spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-07-07 Aparajita Dasgupta, Anirudha Poria
In this paper, we study a class of pseudo-differential operators known as time-frequency localization operators on \({\mathbb {Z}}^n\), which depend on a symbol \(\varsigma \) and two windows functions \(g_1\) and \(g_2\). We define the short-time Fourier transform on \( {\mathbb {Z}}^n \times {\mathbb {T}}^n \) and modulation spaces on \({\mathbb {Z}}^n\), and present some basic properties. Then,
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On Berezin type operators and Toeplitz operators on Bergman spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-07-07 Gabriel T. Prǎjiturǎ, Ruhan Zhao, Lifang Zhou
We introduce a class of integral operators called Berezin type operators. It is a generalization of the Berezin transform, and has a close relation to the Bergman–Carleson measures. The concept is partly motivated by the relationship between Hardy–Carleson measures and area operators. We mainly study the boundedness and the compactness of Berezin type operators from a Bergman space \(A^{p_1}_{\alpha
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Characterizations of Lie derivations on Kadison–Singer algebras Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-07-07 Guangyu An, Rui Zhang, Jun He, Xing Cheng
Kadison–Singer algebra (KS-algebra) is a new class of non-self-adjoint operator algebras. In this paper, we mainly study the standardization of Lie derivations on some KS-algebras. In Sect. 2, we prove that if \({\mathcal {L}}\) is a non-trivial KS-lattice in \(M_{3}(\mathbb {C})\), then every Lie derivation from \(\textrm{Alg}{{\mathcal {L}}}\) into \(M_{3}(\mathbb {C})\) is standard. In Sect. 3,
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Difference of composition operators on the weighted Bergman spaces over the half-plane Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-07-01 Changbao Pang, Zhiyu Wang, Yan Li, Liankuo Zhao
In this paper, based on the characterization of Carleson measure, we study bounded difference of composition operators from Bergman spaces with Békollé weight to Lebesgue spaces over the half-plane. We also obtain a characterization for the Carleson measure by products of functions.
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Helson–Lowdenslager and de Branges type theorems in the setting of continuous rotationally symmetric norms Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-06-22 Apoorva Singh, Niteesh Sahni
A Helson–Lowdenslager type result has been proved by Chen in the context of Lebesgue spaces of the unit circle equipped with a continuous rotationally symmetric norm by studying the simply invariant subspaces of the operator of multiplication by the coordinate function z. In this paper, we generalize Chen’s result by obtaining a description of simply invariant subspaces for multiplication by \(z^n\)
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One-sided invertibility of Toeplitz operators on the space of all holomorphic functions on finitely connected domains Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-06-05 M. Jasiczak
We prove that if the symbol of a Toeplitz operator acting on the space of all holomorphic functions on a finitely connected domain is non-degenerate and vanishes then the range of this operator is not complemented. As a result, we obtain that a Toeplitz operator on the space of all holomorphic functions on finitely connected domains is left invertible if and only if it is an injective Fredholm operator
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Partially defined operators on locally Hilbert spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-05-26 Emanuel-Ciprian Cismas
We investigate partially defined operators on inductive limits of Hilbert spaces, in order to introduce an operator theory for a class of linear operators, outside the Hilbert setting. Some spaces of functions with compact support can fall into the locally Hilbert class and a specific approach is needed for the linear operators compatible with the locally Hilbert structure.
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Schauder frames and completeness of translates in the Orlicz space Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-05-24 Bhawna Dharra, S. Sivananthan
In this paper, we establish the existence of Schauder frames and a result on the completeness of a system of translates of a function in the general setting of Orlicz space. First, we show that for any unbounded set \(\{\lambda _n\}_{n \in {\mathbb {N}}}\), some conditions on the Orlicz function \(\Phi \) ensures the existence of Schauder frames of the form \(\{\tau _{\lambda _n}f,f_n^{*}\}_{n \in
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Semi-Fredholm theory in $$C^{*}$$ -algebras Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-05-18 Stefan Ivković
Kečkić and Lazović introduced an axiomatic approach to Fredholm theory by considering Fredholm type elements in a unital \(C^{*}\)-algebra as a generalization of \(C^{*}\)-Fredholm operators on the standard Hilbert \(C^{*}\)-module introduced by Mishchenko and Fomenko and of Fredholm operators on a properly infinite von Neumann algebra introduced by Breuer. In this paper, we establish semi-Fredholm
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Scaled packing entropy for amenable group actions Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-05-17 Hu Chen, Zhiming Li
In order to characterize the complexity of a system with zero or infinite entropy, we introduce the notions of scaled packing entropies in the framework of countable discrete amenable group actions by describing the speed of divergence of nearby orbits by any scaled sequences. After presenting some basic properties of the scaled packing entropy with respect to the scaled sequences, a variational principle
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Weighted $$L^{p}$$ -boundedness and $$L^{p}$$ -compactness criteria to commutators of operators with kernels satisfying Hörmander type estimates Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-05-16 Li Yang, Qianjun He, Pengtao Li
Let T be a bounded operator on \(L^{p}({\mathbb {R}}^{n})\) and \( A_{p/m'}^{\rho ,\theta }\) denote the class of \(A_{p}\) type weights related with Schrödinger operators \(L=-\Delta +V\), where V belongs to the reverse Hölder class \(B_{q}\). In this paper, under the assumption that the kernel of T satisfies some Hörmander type estimates, we obtain a boundedness criterion for the commutators [b, T]
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Regular measures of noncompactness and Ascoli–Arzelà type compactness criteria in spaces of vector-valued functions Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-05-15 Diana Caponetti, Alessandro Trombetta, Giulio Trombetta
In this paper we estimate the Kuratowski and the Hausdorff measures of noncompactness of bounded subsets of spaces of vector-valued bounded functions and of vector-valued bounded differentiable functions. To this end, we use a quantitative characteristic modeled on a new equicontinuity-type concept and classical quantitative characteristics related to pointwise relative compactness. We obtain new regular
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Real interpolation of variable martingale Hardy spaces and BMO spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-05-13 Jianzhong Lu, Ferenc Weisz, Dejian Zhou
In this paper, we mainly consider the real interpolation spaces for variable Lebesgue spaces defined by the decreasing rearrangement function and for the corresponding martingale Hardy spaces. Let \(0
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Maximal and Calderón–Zygmund operators in grand variable Lebesgue spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-05-11 Shuai Yang, Jiawei Sun, Baode Li
New Banach function spaces \(L^{p(\cdot ),\theta }(X)\) unifying grand Lebesgue spaces and variable Lebesgue spaces are introduced by Kokilashvili and Meskhi. The spaces and operators are defined on quasi-metric finite measure spaces with doubling condition (spaces of homogeneous type). Weighted inequalities with power-type weights in \(L^{p(\cdot ),\theta }(X)\) are obtained for Hardy–Littlewood maximal
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Complete sets in normed linear spaces Banach J. Math. Anal. (IF 1.2) Pub Date : 2023-05-10 Chan He, Horst Martini, Senlin Wu