The aim of this paper is to give several characterizations for the property of weak exponential expansiveness for evolution families in Banach spaces. Variants for weak exponential expansiveness of some well-known results in stability theory (Datko (1973), Rolewicz (1986), Ichikawa (1984), and Megan et al. (2003)) are obtained.

Let N and M be von Neumann algebras. It is proved that L p (N) does not Banach embed in L p (M) for N infinite, M finite, 1 ≤ p < 2. The following considerably stronger result is obtained (which implies this, since the Schatten p-class Cp embeds in L p (N) for N infinite). Theorem. Let 1 ≤ p < 2 and let X be a Banach space with a spanning set (x ij) so that for some C ≥ 1, (i) any row or column...

This paper shows necessary and sufficient conditions on subsets of variable exponent spaces Lp(?)(?) in order to be weakly compact. Useful criteria are given extending Andô results for Orlicz spaces. As application, we prove that all separable Banach-Saks. Also, L-weakly compact inclusions between studied.

In this paper, we have studied the Henstock - Kurzweil integral which is a generalized Riemann means. Hen-stock natural extension of integral. We defined Banach space valued function with respect to bounded variation an real increasing function. investigated elementary properties variation. proved convergence theorems and Saks lemma functions vari-ation. Equi-integrability equi-integrable theor...

We introduce a weakened version of the Dunford-Pettis property, and give examples of Banach spaces with this property. In particular, we show that every closed subspace of Schreier’s space S enjoys it. As an application, we characterize the weak polynomial convergence of sequences, show that every closed subspace of S has the polynomial Dunford-Pettis property of Biström et al. and give other p...

We prove some general results on sequential convergence in Frechet lattices that yield, as particular instances, the following regarding a closed ideal \(I\) of Banach lattice \(E\): (i) If two \(E\), and \(E/I\) have positive Schur property (the property, respectively) then third has well; (ii) dual \(E\) also this property; (iii) weak Dunford-Pettis property. Examples applications are provided.

In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...

In contrast to construction of integrals as limits of Riemann sums, the Gelfand-Pettis characterization is a property no reasonable notion of integral would lack. Since this property is an irreducible minimum, this definition of integral is called a weak integral. Uniqueness of the integral is immediate when the dual V ∗ separates points, meaning that for v 6 v′ in V there is λ ∈ V ∗ with λv 6=...

The main result is that a separable Banach space with the weak∗ unconditional tree property is isomorphic to a subspace as well as a quotient of a Banach space with a shrinking unconditional basis. A consequence of this is that a Banach space is isomorphic to a subspace of a space with an unconditional basis iff it is isomorphic to a quotient of a space with an unconditional basis, which solves...