Positivity最新文献

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.

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 available in the literature and that were established separately so far. We also prove that uniform exponential stability persists under unbounded boundary perturbations. Finally, applications to a Boltzmann equation with non-local boundary conditions on a finite network and a size-dependent population system with delayed birth process are also presented.

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, SMP implies that each (Y_e) has a (pi )-base of clopen sets. The converse fails, but holds if A has a strong unit (and in a somewhat more general situation).

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.