On Some Banach Space Properties Sufficient for Weak Normal Structure and Their Permanence Properties
نویسنده
چکیده
We consider Banach space properties that lie between conditions introduced by Bynum and Landes. These properties depend on the metric behavior of weakly convergent sequences. We also investigate the permanence properties of these conditions.
منابع مشابه
On Some Banach Space Properties Sufficient for Weak Normal Structure and Their Permanence Properties Brailey Sims and Michael A. Smyth
We consider Banach space properties that lie between conditions introduced by Bynum and Landes. These properties depend on the metric behavior of weakly convergent sequences. We also investigate the permanence properties of these conditions.
متن کاملSome properties of b-weakly compact operators on Banach lattices
In this paper we give some necessary and sufficient conditions for which each Banach lattice is space and we study some properties of b-weakly compact operators from a Banach lattice into a Banach space . We show that every weakly compact operator from a Banach lattice into a Banach space is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...
متن کاملWeak Banach-Saks property in the space of compact operators
For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$, it is shown that the strong Banach-Saks-ness of all evaluation operators on ${mathcal M}$ is a sufficient condition for the weak Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in Y^*$, the evaluation op...
متن کاملSome results about unbounded convergences in Banach lattices
Suppose E is a Banach lattice. A net in E is said to be unbounded absolute weak convergent ( uaw-convergent, for short) to provided that the net convergences to zero, weakly. In this note, we further investigate unbounded absolute weak convergence in E. We show that this convergence is stable under passing to and from ideals and sublattices. Compatible with un-convergenc, we show that ...
متن کاملSome notes for topological centers on the duals of Banach algebras
We introduce the weak topological centers of left and right module actions and we study some of their properties. We investigate the relationship between these new concepts and the topological centers of of left and right module actions with some results in the group algebras.
متن کامل