Positivity最新文献

Abstract

Using the connection between ellipsoids and positive semidefinite matrices we provide alternative proofs to some recently proven inequalities concerning the volume of (L_2) zonoids as consequences of classical inequalities for matrices.

A functional calculus for an order complete vector lattice ({mathcal {E}}) was developed by Grobler (Indag Math (NS) 25(2):275–295, 2014) using the Daniell integral. We show that if one represents the universal completion of ({mathcal {E}}) as (C^infty (K)), where K is an extremally disconnected compact Hausdorff topological space, then the Daniell functional calculus for continuous functions is exactly the pointwise composition of functions in (C^infty (K)). This representation allows an easy deduction of the various properties of the functional calculus. Afterwards, we study discrete stopping times and stopped processes in (C^infty (K)). We obtain a representation that is analogous to what is expected in probability theory.

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 some of the difficulties that arise in this context in order to obtain different results related to the existence of mild solutions for this evolution problem.

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.

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 compact operators (mathcal {K(H)}.) We first consider the relationship between the boundary eigenvalues of (Phi _{{mathcal {A}}}|_{mathcal {K(H})}) and its fixed points. Also, we show that the spectra of (Phi _{{mathcal {A}}}) and (Phi _{{mathcal {A}}}|_{mathcal {K(H})}) are the same sets. In particular, the spectra of two completely positive maps involving the unilateral shift are described.

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 for partial transpose of positive semidefinite block matrix are included.

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 behavior of the class of these operators with the weak DP(^*) property of order p (with focus on Banach lattices with the strong limited p-Schur property) is investigated. Moreover, Banach lattices with the positive limited p-Schur property are introduced and Banach lattices in which this property is equivalent to some other known properties are discussed. In addition, the domination properties of almost limited p-convergent and weak(^*) almost p-convergent operators are considered. As an application, using almost limited p-convergent operators we establish some necessary and sufficient conditions under which some operator spaces have the strong limited p-Schur property.

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 the limiting subdifferential. Sufficient conditions for the existence of (weakly) robust efficient solutions to such a problem are also driven under the new concept of pseudo-quasi convexity for composite functions. We formulate a Mond–Weir-type robust dual problem to the primal problem ((text {CUP})), and explore weak, strong, and converse duality properties. In addition, the obtained results are applied to an approximate uncertain multiobjective problem and a composite uncertain multiobjective problem with linear operators.

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.

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.