The main goal of this article is to establish several new \({\mathbb {A}}\)-numerical radius equalities for \(n\times n\) circulant, skew circulant, imaginary circulant, imaginary skew circulant, tridiagonal, and anti-tridiagonal operator matrices, where \({\mathbb {A}}\) is the \(n\times n\) diagonal operator matrix whose diagonal entries are positive bounded operator A. Some special cases of our

We introduce a new norm on the space of all bounded linear operators on a complex Hilbert space, which generalizes the numerical radius norm, the usual operator norm and the modified Davis–Wielandt radius norm. We study basic properties of this norm, including the upper and the lower bounds for it. As an application of the present study, we estimate bounds for the numerical radius of bounded linear

A more accurate half-discrete Hilbert-type inequality in the whole plane with multi-parameters is established by the use of Hermite–Hadamard’s inequality and weight functions. Furthermore, some equivalent forms and some special types of inequalities and operator representations as well as reverses are considered.

We study the norm derivatives in the context of Birkhoff–James orthogonality in real Banach spaces. As an application of this, we obtain a complete characterization of the left-symmetric points and the right-symmetric points in a real Banach space in terms of the norm derivatives. We obtain a complete characterization of strong Birkhoff–James orthogonality in \(\ell _1^n\) and \(\ell _\infty ^n\) spaces

We obtain a Shimorin Wold-type decomposition for a doubly commuting covariant representation of a product system of \(C^*\)-correspondences over \({\mathbb {N}}_0^k\). This result gives Shimorin-type decompositions of recent Wold-type decompositions by Jeu and Pinto (Adv Math 368:107–149, 2020) for the q-doubly commuting isometries and by Popescu (J Funct Anal 279:108798, 2020) for Doubly \(\Lambda

Weighted inequalities with power-type weights for operators of harmonic analysis, such as maximal and singular integral operators, and commutators of singular integrals in grand variable exponent Lebesgue spaces are derived. The spaces and operators are defined on quasi-metric measure spaces with doubling condition (spaces of homogeneous type). The proof of the result regarding the Hardy–Littlewood

In this paper, we study a Bishop–Phelps–Bollobás type property called the property \({\mathbf{L}}_{o,o}\) of a pair of Banach spaces. Getting motivated by this, we introduce the notion of Approximate minimizing property (AMp) of a pair of Banach spaces and characterize finite dimensionality of Banach spaces with respect to this property. We further introduce the notion of approximate minimum norm attainment

We prove sectorial extension theorems for ultraholomorphic function classes of Beurling type defined by weight functions with a controlled loss of regularity. The proofs are based on a reduction lemma, due to the second author, which allows to extract the Beurling from the Roumieu case, which was treated recently by Jiménez-Garrido, Sanz, and the third author. To have control on the opening of the

The invariant subspaces of the Hardy space \(H^2(\mathbb {D})\) of the unit disc are very well known; however, in several variables, the structure of the invariant subspaces of the classical Hardy spaces is not yet fully understood. In this study, we examine the structure of invariant subspaces of Poletsky–Stessin–Hardy spaces which are the generalization of the classical Hardy spaces to hyperconvex

This paper investigates two class of Schrödinger equations with mixed source terms, containing, respectively, a local/non-local non-linearity and an inhomogeneous perturbation. In the energy sub-critical regime, one obtains some sharp thresholds of global/non-global existence dichotomy.

In this paper, We introduce a new class of multivariable operators known as joint m-quasihyponormal tuple of operators. It is a naturel extension of joint normal and joint hyponormal tuples of operators. An m-tuple of operators \(\mathbf{S}=(S_1, \ldots ,S_m)\in {{\mathcal {B}}}({{\mathcal {H}}})^m\) is said to be joint m-quasihyponormal tuple if \(\mathbf{S}\) satisfying $$\begin{aligned} \displaystyle

In this paper, we study an analytic Yeh–Feynman integral and an analytic Yeh–Fourier–Feynman transform associated with Gaussian processes. Fubini theorems involving the generalized analytic Yeh–Feynman integrals are established. The Fubini theorems investigated in this paper are to express the iterated generalized Yeh–Feynman integrals associated with Gaussian processes as a single generalized Yeh–Feynman

This paper presents a systematic study for abstract harmonic analysis on classical Banach spaces of covariant functions of characters of compact subgroups. Let G be a locally compact group and H be a compact subgroup of G. Suppose that \(\xi :H\rightarrow \mathbb {T}\) is a character, \(1\le p<\infty\) and \(L_\xi ^p(G,H)\) is the set of all covariant functions of \(\xi\) in \(L^p(G)\). It is shown

In this paper we provide upper estimates for the global projective dimensions of smooth crossed products \(\mathscr {S}(G, A; \alpha )\) for \(G = \mathbb {R}\) and \(G = \mathbb {T}\) and a self-induced Fréchet–Arens–Michael algebra A. To do this, we provide a powerful generalization of methods which are used in the works of Ogneva and Helemskii.

The primary purpose of this paper is to discuss the g-frame operator distance problems. Specifically, let \(A \in M_{d}({\mathbb {C}})^{+}\) be a positive semidefinite \(d\times d\) complex matrix, \(a=(a_{i})_{i=1}^{n}\in ({\mathbb {R}}^{n}_{\ge 0})^{\downarrow }\) be a n-tuple of positive numbers and \({\mathbb {T}}_{d}(a)\) be a set of g-frames \(G=\{\Lambda _{i}\}_{i=1}^{n}\) such that \(\Vert

We define a tracial analog of the notion called a sequentially split \(^*\)-homomorphism between \(C^*\)-algebras due to Barlak and Szabó and show that several important approximation properties related to the classification theory of \(C^*\)-algebras pass from the target algebra to the domain algebra. Then, we show that this framework arises from tracial Rokhlin properties of a finite group action

In this paper, the necessary and sufficient conditions were given for Orlicz–Lorentz function space endowed with the Orlicz norm having uniformly normal structure and uniform non-squareness.

We pose a conjecture on the K-theory of the self-similar k-graph C*-algebra of a standard product of odometers. We generalize the C*-algebra \({\mathcal {Q}}_S\) to any subset of \({\mathbb {N}}^\times \setminus \{1\}\) and then realize it as the self-similar k-graph C*-algebra of a standard product of odometers.

Let \({\mathcal {A}}\) be an algebra. In this paper, we consider the problem of determining a linear map \(\psi \) on \({\mathcal {A}}\) satisfying \(a,b\in {\mathcal {A}}\), \(ab=0 \Longrightarrow \psi ([a,b])=[\psi (a),b] \, (C1) \) or \(ab=0 \Longrightarrow \psi ([a,b])=[a,\psi (b)] \, (C2)\). We first compare linear maps satisfying (C1) or (C2), commuting linear maps, and Lie centralizers with

We consider the notion of \(\chi\)-completeness of a locally finite graph and we extend this notion to the weighted magnetic graph. Moreover, we establish a link between the magnetic adjacency matrix on line graph and the magnetic discrete Laplacian on 1-forms.

In this paper, we consider the solvability of the system of two operator equations \(AX=C\) and \(XB=D\) in the framework of Hilbert \(C{{}^{*}}\)-modules as well as the existence of Hermitian and positive solutions. We also provide formulae for the general forms of such solutions.

A bounded linear operator A acting on a separable complex Hilbert space H is called C-normal with respect to some conjugation C on H if \(CA^*AC=AA^*\). In the present paper, we show that every bounded linear operator A on H can be perturbed by finite-rank operator F with norm as small as desired so that \(A+F\) is not C-normal with respect to any conjugation C.

In this paper, we introduce the notion of abstract local operator algebras and operator modules, and provide a representation theorem for them which extends the BRS theorem for operator algebras. Furthermore, we give a new proof for the representation theorem of local operator systems. Also, we investigate the Haagerup tensor product of local operator spaces and Morita equivalence of local operator

Let \({\mathcal {H}}={\mathcal {H}}_+\oplus {\mathcal {H}}_-\) be a fixed orthogonal decomposition of the complex separable Hilbert space \({\mathcal {H}}\) in two infinite-dimensional subspaces. We study the geometry of the set \({\mathcal {P}}^p\) of selfadjoint projections in the Banach algebra $${\mathcal {A}}^p=\{A\in {\mathcal {B}}({\mathcal {H}}): [A,E_+]\in {\mathcal {B}}_p({\mathcal {H}})\}

Let X be a completely regular Hausdorff space and \(C_b(X)\) be the space of all bounded continuous functions on X, equipped with the strict topology \(\beta \). We study some important classes of \((\beta ,\Vert \cdot \Vert _E)\)-continuous linear operators from \(C_b(X)\) to a Banach space \((E,\Vert \cdot \Vert _E)\): \(\beta \)-absolutely summing operators, compact operators and \(\beta \)-nuclear

In this paper, we utilize the method of submajorization and the properties of operators to generalize the submajorisation and determinant inequalities of sector matrices to operators in a finite von Neumann algebra.

We first generalize the \({\mathcal {N}}_{\psi }\) quotient modules introduced by Izuchi and Yang to the tridisc and give a characterization of the \({\mathcal {N}}_{\psi }\) quotient modules, and then construct a weighted Bergman bundle shift model introduced firstly by Douglas, Keshari, and the author for the Toeplitz operator \(T_{B}\) with a finite Blaschke product symbol B on the \({\mathcal {N}}_{\psi

In this paper, we investigated the commutators of Hardy–Littlewood maximal function with symbol function b in generalized BMO spaces. Some characterizations of generalized BMO spaces are obtained via the strong and weak boundedness of the commutators on Orlicz–Morrey space.

Following the idea of the paper by Contreras and Hernández-Díaz, we first give the characterization of the boundedness of the weighted composition operator \(W_{\varphi ,\phi }\) on \(B^p\). Then, we investigate the boundedness and the compactness of composition operators \(C_{\varphi}\) on \(B^p\) and study the spectrum of the multiplication operator \(M_{\phi}\) on \(B^p\), as well. Finally, motivated

In this article, we study a generalization of the n-inner product which we name weak n-inner product. As particular case, we consider the n-iterated 2-inner product and we give its representation in terms of the standard k-inner products, \(k\le n\), using the Dodgson’s identity for determinants. Finally, we present several applications, including a brief characterization of a linear regression model

Assume that a convergent series of real numbers \(\sum \limits _{n=1}^\infty a_n\) has the property that there exists a set \(A\subseteq {\mathbb {N}}\) such that the series \(\sum \limits _{n \in A} a_n\) is conditionally convergent. We prove that for a given arbitrary sequence \((b_n)\) of real numbers there exists a permutation \(\sigma :{\mathbb {N}}\rightarrow {\mathbb {N}}\) such that \(\sigma

We obtain bounds for the numerical radius of \(2 \times 2\) operator matrices which improve on the existing bounds. We also show that the inequalities obtained here generalize the existing ones. As an application of the results obtained here, we estimate the bounds for the zeros of a monic polynomial and illustrate with numerical examples that the bounds are better than the existing ones.

In this paper, we study the noncommutative functional equation \(h(\lambda z)-\lambda {h(z)}=g(z),~z\in {\mathbb {C}}\) and we give a new perspective from this equation to obtain a completely dynamical classification for complex matrices. Coarsely speaking, there are four different types: \(0,\frac{1}{2},2\) and \(e^{{\mathbf {i}}2\pi \theta }\) with \(\theta \in [0,\frac{1}{2}]\) for diagonal matrices

In this note, we prove the equalities for the weighted geometric mean of two accretive matrices A and B: $$\begin{aligned} A\sharp _\nu B=B\sharp _{1-\nu }A=A^{\frac{1}{2}}(A^{-\frac{1}{2}}BA^{-\frac{1}{2}})^{\nu }A^{\frac{1}{2}}=B^{\frac{1}{2}}(B^{-\frac{1}{2}}AB^{-\frac{1}{2}})^{1-\nu }B^{\frac{1}{2}},\quad 0<\mathrm{Re\,}\nu <1, \end{aligned}$$ which inherit the same expressions as positive semidefinite

We obtain upper and lower bounds for the Davis-Wielandt radius of bounded linear operators defined on a complex Hilbert space, which improve on the existing ones. We also obtain bounds for the Davis-Wielandt radius of operator matrices. We determine the exact value of the Davis-Wielandt radius of two special type of operator matrices $\left(\begin{array}{cc} I & B 0 & 0 \end{array}\right)$ and $\l

In this paper, we study the Lambert transform over distributions of compact support on $$(0,\infty )$$ . We obtain an inversion formula for this transform and we prove a Parseval-type relation for the Lambert transform of functions in $$L^1 ((0,\infty ))$$ . We also extend this transform to Boehmian spaces.

We study the semi-Hilbertian structure induced by a positive operator A on a Hilbert space $${\mathbb {H}}.$$ Restricting our attention to $$A-$$ bounded positive operators, we characterize the norm attainment set and also investigate the corresponding compactness property. We obtain a complete characterization of the $$A-$$ Birkhoff–James orthogonality of $$A-$$ bounded operators under an additional

We mainly consider the stability and reconstruction of convolution random sampling in multiply generated shift-invariant subspaces $$\begin{aligned} V^{p}(\varPhi )=\left\{ \sum \limits _{k\in \mathbb {Z}^{d}}c(k)^{T}\varPhi (\cdot -k):(c(k))_{k\in \mathbb {Z}^{d}}\in (\ell ^{p}(\mathbb {Z}^{d}))^r \right\} \end{aligned}$$ of \(L^p(\mathbb {R}^{d})\), \(1

In this paper, our central focus is upon a class of linear operators acting on a Banach space X called relatively pseudo weakly demicompact operators. We clarify and determine the relationships with pseudo upper semi-Fredholm and pseudo Fredholm operators. Moreover, a characterization by means of an axiomatic measure of weak noncompactness of linear operators is established. Our results are subsequently

Let X be a nonempty set. A vector sublattice L of $$\mathbb {R}^{X}$$ is said to be truncated if L contains with any function f the function $$ f\wedge \mathbf {1}_{X}$$ . A nonzero linear functional $$\psi $$ on L is called a truncation homomorphism if it preserves truncation (i.e., $$\psi \left( f\wedge \mathbf {1}_{X}\right) =\min \left\{ \psi \left( f\right) ,1\right\} $$ for all $$f\in L$$ ).

We say that a map $T: S_X\rightarrow S_Y$ between the unit spheres of two real normed-spaces $X$ and $Y$ is a phase-isometry if it satisfies \begin{eqnarray*} \{\|T(x)+T(y)\|, \|T(x)-T(y)\|\}=\{\|x+y\|, \|x-y\|\} \end{eqnarray*} for all $x,y\in S_X$. In the present paper, we show that there is a phase function $\varepsilon:S_X\rightarrow \{-1,1\}$ such that $\varepsilon \cdot T$ is an isometry which

We are concerned with the following p-Laplacian equation $$\begin{aligned} -\varDelta _{p} u+|u|^{p-2}u=\mu u+|u|^{s-2}u,~\text {in}~{\mathbb {R}}^{N}, \end{aligned}$$ where $$-\varDelta _{p}u=div(|\nabla u|^{p-2}\nabla u)$$ , $$1

In this paper, we investigate the Hardy-Littlewood maximal function on non-commutative symmetric spaces. We complete the results of T. Bekjan and J. Shao. Moreover, we refine the main results of the papers \cite{Bek} and \cite{Sh}.

In this paper, we investigate the existence of mild solutions to Hilfer fractional equation of semi-linear evolution with non-instantaneous impulses, using the concepts of equicontinuous $C_{0}$-semigroup and Kuratowski measure of non-compactness in Banach space $\Omega$.

Sets in Banach spaces that are mapped into norm compact sets by operators $$T:X\rightarrow \ell _p$$ (called weakly p-Dunford Pettis sets), for $$1< p< \infty $$ , are studied in arbitrary Banach spaces X and in the space $$L_1(\mu , X)$$ of Bochner integrable functions. Sufficient conditions for a subset of $$L_1(\mu , X)$$ to be a weakly p-Dunford Pettis set are given. It is shown that if $$X^*\in

This paper is concerned with the ergodicity and strong stability for (b, l)-regularized resolvent operator families. First, we study Abel ergodicity and Cesáro ergodicity of (b, l)-regularized resolvent operator families by using the methods of operator theory and complex Tauberian theorem. And then, by constructing a new operator-valued function, we obtain some sufficient conditions on the strong

By means of the weight function, the following results are given. The Hilbert-type multiple integral inequality with the $$\lambda $$ -order homogeneous kernel $$\int _{R_{+}^{n}}\int _{R_{+}^{m}}K(\left\| x\right\| _{m,\rho },\left\| y\right\| _{n,\rho })f(x)g(y)\mathrm{d}x\mathrm{d}y\le M\left\| f\right\| _{p,\alpha }\left\| g\right\| _{q,\beta }$$ is true if and only if $$\frac{\alpha +m}{p}+\frac{\beta

We revisit an archive submission by P. B. Denton, S. J. Parke, T. Tao, and X. Zhang, arXiv:1908.03795, on $n \times n$ self-adjoint matrices from the point of view of self-adjoint Dirichlet Schrodinger operators on a compact interval.

Our aim in this paper is to consider a generalization of the concept of n-quasi-m-isometric operators of a single operator done in Mahmoud Sid Ahmed et al. (Results Math 73:511–531, 2018) and Mechri and Mahmoud Sid Ahmed (Oper Matrices 14(1): 145–157, 2020) to the multi-dimensional operators. We discuss the most interesting results concerning these classes of tuples of operators by extending some results

For a Young function $$\phi $$ and a locally compact second countable group G, let $$L^\phi (G)$$ denote the Orlicz space on G. In this paper, we present a necessary and sufficient condition for the topological transitivity of a sequence of cosine operators $$\{C_n\}_{n=1}^{\infty }:=\{\frac{1}{2}(T^n_{g,w}+S^n_{g,w})\}_{n=1}^{\infty }$$ , defined on $$L^{\phi }(G)$$ . We investigate the conditions

By a new method derived from Nicola--Primo--Tabacco[24], we study the boundedness on $\alpha$-modulation spaces of unimodular multipliers with symbol $e^{i\mu(\xi)}$. Comparing with the previous results, the boundedness result is established for a larger family of unimodular multipliers under weaker assumptions.

In this paper, we discuss new inequalities for accretive matrices through non-standard domains. In particular, we present several relations for $$A^r$$ and $$A\sharp _rB$$ , when A, B are accretive and $$r\in (-1,0)\cup (1,2).$$ This complements the well-established discussion of such quantities for accretive matrices when $$r\in [0,1],$$ and provides accretive versions of known results for positive

The original article has been corrected.

In this paper, we consider the non-spectral problem for the planar self-affine measures $$\mu _{M,D}$$ generated by an expanding integer matrix $$M\in M_2({\mathbb {Z}})$$ and a finite digit set $$\begin{aligned} D=\{(0,0)^t, (\alpha _1,\alpha _2)^t, (\alpha _3, \alpha _4)^t \} \oplus k(\alpha _1\alpha _4-\alpha _2\alpha _3){\mathfrak {D}}, \end{aligned}$$ where $$k\in {\mathbb {Z}}\backslash \{0\}

The notion of conjugation is extended to Banach $$*$$ -algebras. The aim of this paper is to characterize conjugations on the Banach algebra of all bounded linear operators on a complex Hilbert space, the algebra of J-symmetric operators on a complex Hilbert space with given conjugation J and the algebra of all complex valued continuous functions, defined on a connected locally compact Hausdorff space

Let A and B be $$n\times n$$ positive semidefinite matrices, and let $$ \alpha ,\beta \in (0,1)$$ such that $$\alpha +\beta =1$$ . Among other inequalities, it is shown that

It is known in the literature that in the RNP Banach space the set valued uniformly integrable martingale is a regular martingale. In this paper by using a selector approach we provide a weaker condition than uniform integrability of a set valued Aumann–Pettis integrable martingale to be a set valued Aumann–Pettis integrable regular martingale. The Converse is also established. As an application of

We present a novel generalization, in Banach spaces, of the celebrated Helly’s principle selection. Specifically, our main result is a quantitative version of such principle selection. Our main tool is the so called Degree of Nondensifiability, which measures (in the specified sense) the distance of a given convex subset of a Banach space to the class of its Peano Continua. As application of our results

Let $\sigma$ be a non-trivial operator mean in the sense of Kubo and Ando, and let $OM_+^1$ the set of normalized positive operator monotone functions on $(0, \infty)$. In this paper, we study class of $\sigma$-subpreserving functions $f\in OM_+^1$ satisfying $$f(A\sigma B) \le f(A)\sigma f(B)$$ for all positive operators $A$ and $B$. We provide some criteria for $f$ to be trivial, i.e., $f(t)=1$ or

In this paper, we improve the order of approximation of certain operators linking Bernstein and genuine Bernstein–Durrmeyer operators. Firstly, we obtain some direct results in terms of modulus of continuity and Voronovskaja type asymptotic formula for these operators. Finally, we give some numerical examples regarding the obtained theoretical results for new constructed operators.