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Lebesgue spaces with variable exponent: some applications to the Navier–Stokes equations Positivity (IF 1.0) Pub Date : 2024-03-18 Diego Chamorro, Gastón Vergara-Hermosilla
In this article we study some problems related to the incompressible 3D Navier–Stokes equations from the point of view of Lebesgue spaces of variable exponent. These functional spaces present some particularities that make them quite different from the usual Lebesgue spaces: indeed, some of the most classical tools in analysis are not available in this framework. We will give here some ideas to overcome
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Some new results about order Fredholm theory in Banach lattices Positivity (IF 1.0) Pub Date : 2024-03-16 Youssef Ezzaki, Othman Aboutafail, Jawad H’michane
This paper aims to introduce and study a new generalized class of semi-Fredholm operators acting between Banach lattices called order semi-Fredholm operators. It highlights some interesting properties of this class. Also, a perturbation properties are obtained. Finally, we discuss the conditions that make the adjoint of an order semi-Fredholm operator be a semi-Fredholm operator.
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On spectra of some completely positive maps Positivity (IF 1.0) Pub Date : 2024-03-15 Yuan Li, Shuhui Gao, Cong Zhao, Nan Ma
Let \(\sum _{i=1}^{\infty }A_iA_i^*\) and \(\sum _{i=1}^{\infty }A_i^*A_i\) converge in the strong operator topology. We study the map \(\Phi _{{\mathcal {A}}}\) defined on the Banach space of all bounded linear operators \({\mathcal {B(H)}}\) by \(\Phi _{{\mathcal {A}}}(X)=\sum _{i=1}^{\infty }A_iXA_i^*\) and its restriction \(\Phi _{{\mathcal {A}}}|_{\mathcal {K(H})}\) to the Banach space of all
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On almost limited p-convergent operators on Banach lattices Positivity (IF 1.0) Pub Date : 2024-03-14 H. Ardakani, F. Vali
The purpose of this article is to introduce and study the class of almost limited p-convergent and weak\(^*\) almost p-convergent operators (\(1 \le p <\infty \)). Some new characterizations of Banach lattices with the strong limited p-Schur property; that is, spaces on which every almost limited weakly p-compact set is relatively compact and the weak DP\(^*\) property of order p are obtained. The
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Partial trace inequalities for partial transpose of positive semidefinite block matrices Positivity (IF 1.0) Pub Date : 2024-03-14 Junjian Yang, Huan Xu
Li (Algebra 71:2823–2838, 2023) recently obtained several improvements on some partial trace inequalities for positive semidefinite block matrices. In this note, we present analogous partial trace inequalities involving partial transpose of positive semidefinite block matrix. The inequalities we show could be regarded as complements of Li’s results. In addition, some new partial trace inequalities
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Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications Positivity (IF 1.0) Pub Date : 2024-03-08 Maryam Saadati, Morteza Oveisiha
This article is devoted to investigate a nonsmooth/nonconvex uncertain multiobjective optimization problem with composition fields (\((\text {CUP})\) for brevity) over arbitrary Asplund spaces. Employing some advanced techniques of variational analysis and generalized differentiation, we establish necessary optimality conditions for weakly robust efficient solutions of \((\text {CUP})\) in terms of
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On the norm bounded sets of the ideal $$E^{a}$$ Positivity (IF 1.0) Pub Date : 2024-03-04
Abstract The paper is devoted to study the norm bounded subsets which are contained in \(E^{a}\) . Also, we introduce and study the class of the bounded- \(E^a\) operators, which maps the closed unit ball of a Banach space to a subset of \(E^{a}\) . Some interesting results about this class of operators are presented.
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Some results on upper semi-Fredholm operators on Banach lattices Positivity (IF 1.0) Pub Date : 2024-02-29 Youssef Ezzaki, Redouane Nouira, Othman Aboutafail
We study the class of upper semi-Fredholm operators acting between Banach lattices. It focuses on the domination of such operators by compact, Dunford–Pettis and AM-compact operators.
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Well-posedness and stability of a class of linear systems Positivity (IF 1.0) Pub Date : 2024-02-28 Yassine El Gantouh
The aim of this work is to provide useful criteria for well-posedness, positivity and stability of a class of infinite-dimensional linear systems. These criteria are based on an inverse estimate with respect to the Hille–Yosida Theorem. Indeed, we establish a generation result for perturbed positive operator semigroups, namely, for positive unbounded boundary perturbations. This unifies previous results
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The Freudenthal spectral theorem and sufficiently many projections in Archimedean vector lattices Positivity (IF 1.0) Pub Date : 2024-02-25 Anthony W. Hager, Brian Wynne
The Yosida representation for an Archimedean vector lattice A with weak unit u, denoted (A, u), reveals similarities between the ideas of the title, FST and SMP. If A is Archimedean, the conclusion of the FST means exactly that for each \(0 < e \in A\), the Yosida space for \((e^{dd},e)\), denoted \(Y_e\), has a base of clopen sets. This yields a short “Yosida based" proof of FST. On the other hand
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Nonlinear operator extensions of Korovkin’s theorems Positivity (IF 1.0) Pub Date : 2024-02-23 Sorin G. Gal, Constantin P. Niculescu
In this paper we extend Korovkin’s theorem to the context of sequences of weakly nonlinear and monotone operators defined on certain Banach function spaces. Several examples illustrating the theory are included.
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A characterization of two-weight norm inequalities for multidimensional Hausdorff operators on Lebesgue spaces Positivity (IF 1.0) Pub Date : 2024-02-21 Rovshan Bandaliyev, Dunya Aliyeva
In this paper we give necessary and sufficient conditions for the boundedness of the multidimensional Hausdorff operator on weighted Lebesgue spaces. In particular, we establish necessary and sufficient conditions for the boundedness of special type of the multidimensional Hausdorff operator on weighted Lebesgue spaces for monotone radial weight functions. Also, we get similar results for important
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Extensions of Nazarov–Podkorytov lemma in non-commutative spaces of $$\tau $$ -measurable operators Positivity (IF 1.0) Pub Date : 2024-02-07
Abstract In this work, we study a comparison of norms in non-commutative spaces of \(\tau \) -measurable operators associated with a semifinite von Neumann algebra. In particular, we obtain Nazarov–Podkorytov type lemma Nazarov et al. (Complex analysis, operators, and related topics. Operatory theory: advances, vol 113, pp 247–267, 2000) and extend the main results in Astashkin et al. (Math Ann, 2023
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Splitting of conditional expectations and liftings in product spaces Positivity (IF 1.0) Pub Date : 2024-01-28 Kazimierz Musiał
Let \((X, {{\mathfrak {A}}},P)\) and \((Y, {{\mathfrak {B}}},Q)\) be two probability spaces and R be their skew product on the product \(\sigma \)-algebra \({{\mathfrak {A}}}\otimes {{\mathfrak {B}}}\). Moreover, let \(\{({{\mathfrak {A}}}_y,S_y):y\in {Y}\}\) be a Q-disintegration of R (if \({{\mathfrak {A}}}_y={{\mathfrak {A}}}\) for every \(y\in {Y}\), then we have a regular conditional probability
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Order theoretical structures in atomic JBW-algebras: disjointness, bands, and centres Positivity (IF 1.0) Pub Date : 2024-01-19
Abstract Every atomic JBW-algebra is known to be a direct sum of JBW-algebra factors of type I. Extending Kadison’s anti-lattice theorem, we show that each of these factors is a disjointness free anti-lattice. We characterise disjointness, bands, and disjointness preserving bijections with disjointness preserving inverses in direct sums of disjointness free anti-lattices and, therefore, in atomic JBW-algebras
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A Fock space approach to the theory of kernel functions Positivity (IF 1.0) Pub Date : 2024-01-17 Michio Seto
In this paper, we give a new approach to the theory of kernel functions. Our method is based on the structure of Fock spaces. As its applications, two non-Euclidean examples of strictly positive kernel functions are given. Moreover, we give a new proof of the universal approximation theorem for Gaussian type kernels.
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The lateral order on Riesz spaces and orthogonally additive operators. II Positivity (IF 1.0) Pub Date : 2024-01-12 Volodymyr Mykhaylyuk, Marat Pliev, Mikhail Popov
The present paper aims to describe the relationships between the intersection property, introduced and studied in the previous paper by the authors, with other known properties of Riesz spaces, and to prove that every lateral ideal of a Riesz space is a kernel of some positive orthogonally additive operator (it is easy to see that the kernel of every positive orthogonally additive operator is a lateral
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Hadamard well-posedness and stability in set optimization Positivity (IF 1.0) Pub Date : 2024-01-12 Meenakshi Gupta, Manjari Srivastava
In this paper, we introduce two kinds of Hadamard well-posedness for a set optimization problem by taking into consideration perturbations of objective function and a relationship between these two well-posedness is derived. Using the generalized Gerstewitz function, a sequence of scalar optimization problems have been defined and a convergence result is obtained. Sufficient conditions for Hadamard
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On unbounded order continuous operators 2 Positivity (IF 1.0) Pub Date : 2023-11-27 Bahri Turan, Hüma Gürkök
Let E and F be two Archimedean Riesz spaces. An operator \(T:E\rightarrow F\) is said to be unbounded order continuous (uo-continuous), if \(u_{\alpha }\overset{uo}{\rightarrow }0\) in E implies \(Tu_{\alpha }\overset{uo}{ \rightarrow }0\) in F. In this study, our main aim is to give the solution to two open problems which are posed by Bahramnezhad and Azar. Using this, we obtain that the space \(L_{uo}(E
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Strictly positive definite non-isotropic kernels on two-point homogeneous manifolds: the asymptotic approach Positivity (IF 1.0) Pub Date : 2023-11-26 J. C. Guella, J. Jäger
We present sufficient conditions for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their expansion in eigenfunctions of the Laplace–Beltrami operator. We also present a characterisation of this kernel class. The family analyzed is a generalization of the isotropic kernels and the case of a real sphere is analyzed in details
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The interplay between algebras and lattices: Stone–Weierstrass for illustration Positivity (IF 1.0) Pub Date : 2023-11-09 Sameh Bououn
We illustrate the interplay between multiplicative structure and ordered structure on Banach spaces of real-valued functions via various versions of the Stone–Weierstrass Approximation Theorem.
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Near order and metric-like functions on the cone of positive definite matrices Positivity (IF 1.0) Pub Date : 2023-11-07 Raluca Dumitru, Jose A. Franco
In this article we introduce a new relation on the cone of positive definite matrices and we study its properties and its effect on operator monotonicity and convexity. Furthermore, we use this new relation to establish analogies between the weighted geometric means \(A\sharp _t B\) and the spectral weighted geometric means \(A\natural _t B\) of positive definite matrices A and B, via the Thompson
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On scalarization and well-posedness in set optimization with a partial set order relation Positivity (IF 1.0) Pub Date : 2023-11-05 Sakshi Gupta, Rekha Gupta, Manjari Srivastava
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On the uniqueness of continuous positive solution for a non-linear integral equation whose singularity lies in the reciprocal of the solution Positivity (IF 1.0) Pub Date : 2023-10-15 Indranil Sarkar, Gaurav Singh
In this article, we consider the following non-linear singular integral equation $$\begin{aligned} y(t)=f(t)+\int _{0}^{1}k(t,s)\frac{1}{[y(s)]^{\alpha }}\text {d}s \end{aligned}$$ in the space of continuous functions on a bounded and closed interval [0, 1] for \(f\in C[0,1]\) with \(f> 0\), the kernel k(t, s) is a non-negative continuous function on \([0,1]\times [0,1]\) and \(\alpha >0\) fixed parameter
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Tensorial representation of p-regular multilinear operators between Banach lattices Positivity (IF 1.0) Pub Date : 2023-10-17 Elhadj Dahia
We introduce the new class of the \((p;p_{1},...,p_{m})\)-regular multilinear operators between Banach lattices, that is defined using a summability property that provides the multilinear version of the (p, q)-regular operators. Some composition results are proved and we show that every continuous multilinear operators are \( (p;p_{1},...,p_{m})\)-regular under some requirements. We find the trace
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On logarithms of measures Positivity (IF 1.0) Pub Date : 2023-10-16 H. Raubenheimer, J. van Appel
Let A be a Banach algebra and let \(x\in A\) have the property that its spectrum does not separate 0 from infinity. It is well known that x has a logarithm, i.e., there exists \(y\in A\) with \(x=e^y\). We will use this statement to identify measures defined on a locally compact group to have logarithms. Also, we will show that the converse of the above statement is in general not true. Our results
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A new result on boundedness of the Riesz potential in central Morrey–Orlicz spaces Positivity (IF 1.0) Pub Date : 2023-10-11 Evgeniya Burtseva, Lech Maligranda
We improve our results on boundedness of the Riesz potential in the central Morrey–Orlicz spaces and the corresponding weak-type version. We also present two new properties of the central Morrey–Orlicz spaces: nontriviality and inclusion property.
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A note on the remainder in the approximation of functions by some positive linear operators Positivity (IF 1.0) Pub Date : 2023-10-06 Marius-Mihai Birou
In this note we give representations for the remainder in approximations formulas generated by positive linear operators which preserve some functions including linear functions. We show that in these cases the Peano kernel from the integral representation of the remainder has the same sign on the definition domain. Applications to the iterates of some positive linear operators and quadrature formulas
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Almost everywhere convergence of the iterates of a bi-stochastic Markov operator Positivity (IF 1.0) Pub Date : 2023-09-30 Yukiko Iwata
We consider a positive contraction P defined on a probability space \((X,\Sigma ,m)\) and assume \(P{\textbf{1}}_X={\textbf{1}}_X\) and \(P^*{\textbf{1}}_X={\textbf{1}}_X\) (i.e., P is a bi-stochastic Markov operator). By virtue of the zero-two law, there exists a sufficient condition for the asymptotic periodicity of P. In this paper, we give some conditions between the convergence almost everywhere
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Disjointly weak compactness in Banach lattices Positivity (IF 1.0) Pub Date : 2023-09-28 Bo Xiang, Jin Xi Chen, Lei Li
We give some characterizations of disjointly weakly compact sets in Banach lattices, namely, those sets in whose solid hulls every disjoint sequence converges weakly to zero. As an application, we prove that a bounded linear operator from a Banach space to a Banach lattice is an almost (L) limited operator if and only if it is a disjointly weakly compact operator, indeed, an operator which carries
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Operator monotone functions on accretive matrices Positivity (IF 1.0) Pub Date : 2023-09-29 Amir Ghasem Ghazanfari, Somayeh Malekinejad
Let \(f: (0,\infty )\rightarrow {\mathbb {R}}\) be an operator monotone function and \(A \in {\mathbb {M}}_n\) be accretive matrix, we show that $$\begin{aligned} f(A)=a+b A+\int _0^\infty \lambda A(\lambda +A)^{-1}d\mu (\lambda ), \end{aligned}$$ where \(b\ge 0\), \(a\in {\mathbb {R}}\) and \(\mu \) is a positive measure on the closed positive half-line \([0,\infty )\) with \(\int \frac{\lambda }{1+\lambda
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Some remarks on orthogonally additive operators Positivity (IF 1.0) Pub Date : 2023-08-29 Olena Fotiy, Vladimir Kadets, Mikhail Popov
We study orthogonally additive operators on Riesz spaces. Our first result gives necessary and sufficient conditions on a pair of Riesz spaces (E, F) for which every orthogonally additive operator from E to F is laterally-to-order bounded. Second result extends an analogue of Pitt’s compactness theorem obtained by the second and third named authors for narrow linear operators to the setting of orthogonally
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Strong comparison and strong maximum principles for quasilinear elliptic equations with a gradient term Positivity (IF 1.0) Pub Date : 2023-08-26 Phuong Le
In this paper, we prove strong comparison principles for the quasilinear elliptic equation $$\begin{aligned} -\Delta _p u + a(u) |\nabla u|^q = f(u), \quad u>0 \quad \text { in } \Omega , \end{aligned}$$ where \(\frac{2N+2}{N+2}< p < 2\), \(q\ge 1\), \(\Omega \) is a bounded domain of \(\mathbb {R}^N\) and a, f satisfy some relevant conditions. We also prove a strong maximum principle for the corresponding
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On the solvability of a cantilever-type boundary value problem by using the mixed monotone operator Positivity (IF 1.0) Pub Date : 2023-08-24 J. Harjani, B. López, K. Sadarangani
In the present paper, by using the mixed monotone operator method we prove the existence and uniqueness of positive solution to the following cantilever-type boundary value problem $$\begin{aligned} \displaystyle \left\{ \begin{array}{l} u^{(4)}(t)=f(t,u(t),u(\alpha t))+g(t,u(t)),\quad 0
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On the convergence of Kantorovich operators in Morrey spaces Positivity (IF 1.0) Pub Date : 2023-08-08 Mu’afa Purwa Arsana, Reinhart Gunadi, Denny Ivanal Hakim, Yoshihiro Sawano
In this paper, we investigate Kantorovich operators on Morrey spaces. We first recall the main tool in the proof of the uniform boundedness of Kantorovich operators in Morrey spaces, namely a pointwise estimate of Kantorovich operators by the Hardy–Littlewood maximal operator. We also investigate the convergence of Kantorovich operators in Morrey spaces under weaker assumptions that is also true for
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Order continuity and regularity on vector lattices and on lattices of continuous functions Positivity (IF 1.0) Pub Date : 2023-08-07 Eugene Bilokopytov
We give several characterizations of order continuous vector lattice homomorphisms between Archimedean vector lattices. We reduce the proofs of some of the equivalences to the case of composition operators between vector lattices of continuous functions, and we obtain a characterization of order continuity of such operators. Motivated by this, we investigate various properties of the sublattices of
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Schoenberg correspondence for k-(super)positive maps on matrix algebras Positivity (IF 1.0) Pub Date : 2023-08-03 B. V. Rajarama Bhat, Purbayan Chakraborty, Uwe Franz
We prove a Schoenberg-type correspondence for non-unital semigroups which generalizes an analogous result for unital semigroup proved by Schürmann (in: Quantum probability and applications II, proceedings of a 2nd workshop, Heidelberg/Germany 1984, lecture notes in mathematics, vol 1136, pp 475–492, 1985). It characterizes the generators of semigroups of linear maps on \(M_n(\mathbb {C})\) which are
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On optimality conditions and duality for multiobjective optimization with equilibrium constraints Positivity (IF 1.0) Pub Date : 2023-07-27 P. Q. Khanh, L. T. Tung
In this paper, we consider nonsmooth multiobjective optimization problems with equilibrium constraints. Necessary/sufficient conditions for optimality in terms of the Michel-Penot subdifferential are established. Then, we propose Wolfe- and Mond–Weir-types of dual problems and investigate duality relations under generalized convexity assumptions. Some examples are provided to illustrate our results
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On optimality conditions and duality for multiobjective optimization with equilibrium constraints Positivity (IF 1.0) Pub Date : 2023-07-21 P. Q. Khanh, L. T. Tung
In this paper, we consider nonsmooth multiobjective optimization problems with equilibrium constraints. Necessary/sufficient conditions for optimality in terms of the Michel-Penot subdifferential are established. Then, we propose Wolfe- and Mond–Weir-types of dual problems and investigate duality relations under generalized convexity assumptions. Some examples are provided to illustrate our results
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Substitution conditional type operators on $$L^2(\Sigma )$$ Positivity (IF 1.0) Pub Date : 2023-07-17 M. R. Jabbarzadeh, L. Farzi
In this paper point spectrum, compactness, reducibility, generalized inverse and some weak normal classes of substitution conditional type operators acting on \(L^{2}(\Sigma )\) will be investigated.
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Projective positivity of the function systems Positivity (IF 1.0) Pub Date : 2023-07-14 Anar Dosi
The present paper is devoted to the projective positivity in the category of function systems, which plays a key role in the quantization problems of the operator systems. The main result of the paper asserts that every unital \(*\)-normed space can be equipped with the projective positivity. The geometry of the related state spaces is described in the case of \(L^{p} \)-spaces, Schatten matrix spaces
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Singular value problems under nonnegativity constraints Positivity (IF 1.0) Pub Date : 2023-07-12 Alberto Seeger, David Sossa
Let A be a real matrix of size \(m\times n\). In classical linear algebra, a real number \(\sigma \) is called a singular value of A if there exist unit vectors \(u\in \mathbb {R}^m\) and \(v\in \mathbb {R}^n\) such that \(Av = \sigma u\) and \( A^\top u = \sigma v\). In variational analysis, a singular value of A is viewed as a critical value of the bilinear form \(\langle u,Av\rangle \) when u and
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On Banach space norms for $${\mathcal {I}}$$ -bounded sequences and their quotient Positivity (IF 1.0) Pub Date : 2023-06-27 Jeff Connor, Fath Temzsu
In this note we establish that, for an an admissible ideal \(\mathcal {I}\), the \(\mathcal {I{\text {-}}\limsup }\) can be used to give a norm which generates a Banach space topology for the quotient of the \(\mathcal {I}\)-bounded sequences modulo the \(\mathcal {I}\)-null sequences via an elementary proof. Also the \(\mathcal {I}\)-bounded and \(\mathcal {I}\)-null sequences cannot, in general,
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On the domination problem of positive Null almost L-weakly compact operators on Banach lattices Positivity (IF 1.0) Pub Date : 2023-06-15 El Aloui Abdennabi, Bouras Khalid
We give a necessary and sufficient conditions for which the domination problem admits a positive solution for the class of positive Null almost L-weakly compact operators, this study ends with an open question which will discussed later. We then consider, the linear span of positive Null almost L-weakly (resp., Null almost M-weakly) compact operators and give results about when they form a Banach lattice
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On separability of the unbounded norm topology Positivity (IF 1.0) Pub Date : 2023-06-01 M. Kandić, A. Vavpetič
In this paper we continue the investigation of topological properties of the unbounded norm (un-)topology in normed lattices. We characterize separability and second countability of the un-topology in terms of properties of the underlying normed lattice. We apply our results to prove that an order continuous Banach function space X over a semi-finite measure space is separable if and only if it has
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Multipliers for global Morrey spaces Positivity (IF 1.0) Pub Date : 2023-05-25 Evgenii I. Berezhnoi
Based on a new approach for a wide class of global Morrey spaces, we give an exact description of the multiplier space between two Morrey spaces from this class. It is shown that in this case the multiplier space for a couple of Morrey spaces is an approximation Morrey space structurally constructed from the original spaces.
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Spectral behaviour of the matrix $$\left[ f(1- p_ip_j)\right] $$ Positivity (IF 1.0) Pub Date : 2023-05-22 Isha Garg, Himanshu Agarwal
Rigorous work on pattern-based special classes of matrices such as \(P_r =[(p_i+p_j)^r]\), \(B_r= [\mid p_i-p_j\mid ^r]\), etc. shows their spectral behavior and beneficial results in the literature. Bhatia and Jain in 2015 and Dyn, Goodman, and Micchelli in 1986 studied the spectral behavior of \(P_r\) and \(B_r\) with respect to power function \(t\rightarrow t^r\) for distinct positive real numbers
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Convex duality for partial hedging of American options: continuous price processes Positivity (IF 1.0) Pub Date : 2023-05-21 Ari-Pekka Perkkiö, Erick Treviño-Aguilar
Partial hedging of American options is an interesting minimax problem and in this paper we establish its dual problem that concerns only maximization. The case of a continuous price process is considered under a general incomplete market. Our construction of a duality requires a careful preparation in order to define the dual domain with a compactness property. A key step is an extension of linear
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Direct limits in categories of normed vector lattices and Banach lattices Positivity (IF 1.0) Pub Date : 2023-05-20 Chun Ding, Marcel de Jeu
After collecting a number of results on interval and almost interval preserving linear maps and vector lattice homomorphisms, we show that direct systems in various categories of normed vector lattices and Banach lattices have direct limits, and that these coincide with direct limits of the systems in naturally associated other categories. For those categories where the general constructions do not
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Some new $$(H_p-L_p)$$ type inequalities for weighted maximal operators of partial sums of Walsh–Fourier series Positivity (IF 1.0) Pub Date : 2023-05-16 Davit Baramidze, Lars-Erik Persson, George Tephnadze
In this paper we introduce some new weighted maximal operators of the partial sums of the Walsh–Fourier series. We prove that for some “optimal” weights these new operators indeed are bounded from the martingale Hardy space \(H_{p}(G)\) to the Lebesgue space \(L_{p}(G),\) for \(0
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A note on “Levitin–Polyak well-posedness in set optimization concerning Pareto efficiency” [Positivity.25(2021), 1923–1942] Positivity (IF 1.0) Pub Date : 2023-05-16 Wenqing Wang, Yihong Xu
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Sharp bounds for multilinear fractional integral operators on Morrey type spaces: the endpoint cases Positivity (IF 1.0) Pub Date : 2023-05-16 Suting Zheng, Dinghuai Wang, Xi Hu
In this paper, the Strichartz’s result of the exponential integrability of fractional integral operators is improved. Also, we establish the endpoint boundedness of the multilinear fractional integrals acting on the multi-Morrey spaces. The conclusions relax the restriction that \(p_{i}\ne 1\) for all \(i=1,\ldots ,m\) and extend some known results.
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Subscalarity for extension of totally polynomially posinormal operators Positivity (IF 1.0) Pub Date : 2023-05-09 T. Prasad
An operator \(T\in B(\mathcal {H})\) is called an analytic root of a totally polynomially posinormal operator if there is a nonconstant complex-valued analytic function F on a neighborhood of \(\sigma (T)\) such that F(T) is totally polynomially posinormal. We prove that analytic roots of totally polynomially posinormal operators under a condition have scalar extensions. As a consequence, we show that
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Existence of positive solutions for a class of elliptic problems with fast increasing weights and critical exponent discontinuous nonlinearity Positivity (IF 1.0) Pub Date : 2023-05-08 Vinicius P. Bandeira, Giovany M. Figueiredo, Gelson C. G. dos Santos
In this paper, using variational methods, we show the existence of at least two nonnegative solutions to a class of elliptic problems with fast increasing weights given by $$\begin{aligned} -\Delta u - \frac{1}{2}(x \cdot \nabla u) = \lambda h(x) + H(u-a)|u|^{2^{*}-2}u \ \text{ in } \ \mathbb {R}^{N}, \end{aligned}$$ where \(a>0,\) \(2^*:=2N/(N-2);\) \(N\ge 3\), \(h:\mathbb {R^{N}}\rightarrow \mathbb
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Some new results on LW-compact operators Positivity (IF 1.0) Pub Date : 2023-04-03 Abdennabi EL Aloui, Khalid Bouras, Aziz Elbour, Farid Afkir
We establish some characterisations of the class of LW-compact operators on Banach lattices and we study the domination for this class.
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Ideals, bands and direct sum decompositions in mixed lattice vector spaces Positivity (IF 1.0) Pub Date : 2023-04-03 Jani Jokela
A mixed lattice vector space is a partially ordered vector space with two partial orderings and certain lattice-type properties. In this paper we first give some fundamental results in mixed lattice groups, and then we investigate the structure theory of mixed lattice vector spaces, which can be viewed as a generalization of the theory of Riesz spaces. More specifically, we study the properties of
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Generalized fractional maximal operators on Musielak-Orlicz-Morrey spaces Positivity (IF 1.0) Pub Date : 2023-03-29 Yoshihiro Mizuta, Takao Ohno, Tetsu Shimomura
We prove the boundedness of the generalized fractional maximal operator \(M_{\rho }\) on Musielak-Orlicz-Morrey spaces, where \(\rho (x,r)\) is a positive function on \(\textbf{R}^N \times (0, \infty )\) satisfying certain conditions. What is new in the present paper is Sobolev and Trudinger type inequalities for \(M_{\rho }\) on non-doubling Musielak-Orlicz-Morrey spaces.
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A study of certain class of strictly positives definite functions and applications Positivity (IF 1.0) Pub Date : 2023-03-26 Khaled Mehrez
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Galois extensions and $$O^{*}$$ -fields Positivity (IF 1.0) Pub Date : 2023-03-23 Kenneth Evans, Jingjing Ma
A field F is \(O^{*}\) if each partial order that makes F a partially ordered field can be extended to a total order that makes F a totally ordered field. We use the theory of infinite primes developed by Dubois and Harrison to prove the following. For a subfield F of \(\mathbb {C}\) that is finite-dimensional over \(\mathbb {Q}\), we prove that when F is Galois over \(\mathbb {Q}\), F is an \(O^{*}\)-field
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Some new results on L-weakly compact sets and applications Positivity (IF 1.0) Pub Date : 2023-03-22 Hassan Khabaoui, Kamal El Fahri, Jawad H’michane
The paper is devoted to study the relationship between limited (resp. (L)) sets and L-weakly compact sets, it rests essentially on two parts. In the first one, we introduce and study the operators which send L-weakly compact sets to limited sets and conversely limited sets to L-weakly compact sets. As consequences, we will give some interesting results. In the second part, we look at the dual counterpart