A subsequence principle is obtained, characterizing Banach spacescontaining co' in the spirit of the author's 1974 characterization of Banachspaces containing II . Defiaition. A sequence(bj )in a Banach space is called strongly summing (s.s.)if (bj ) is a weak-Cauchy basic sequence so that whenever scalars (cj ) satisfysUPn II E~=I cijll < 00, thenECj converges.A...

In this note we prove that the weak topology of a Banach space has the Continuous Representability Property which means that every (weakly) continuous total preorder defined on a Banach space can be represented by a weakly continuous utility function. This shows that weak topologies are perfect to look for continuous utility functions that represent preferences on infinite-dimensional commodity...

A subsequence principle is obtained, characterizing Banach spacescontaining co' in the spirit of the author's 1974 characterization of Banachspaces containing II . Defiaition. A sequence(bj )in a Banach space is called strongly summing (s.s.)if (bj ) is a weak-Cauchy basic sequence so that whenever scalars (cj ) satisfysUPn II E~=I cijll < 00, thenECj converges.A...

We look for geometric structures which underlie both the 'classical' geometric and more modern 'order theoretic' conditions for a Banach space (dual space) to have the weak (weak*) fixed point property; that is, for every nonexpansive self-mapping of a nonempty weak (weak*) compact convex subset to have a fixed point.

In this article we define measurable multifunctions in nonseparable Banach spaces, prove a weak compactness criterion for the selectors of multifunctions integrably bounded, characterize Banach spaces that have the Radon–Nikodym property by means of convergence of multivalued martingales, generalize some recent results on convergence of set-valued conditional expectations, and give some applica...

The implicit midpoint rule (IMR) for nonexpansive mappings is established in Banach spaces. The IMR generates a sequence by an implicit algorithm. Weak convergence of this algorithm is proved in a uniformly convex Banach space which either satisfies Opial’s property or has a Fréchet differentiable norm. Consequently, this algorithm applies in both `p and Lp for 1 < p < ∞.

In this study, some existing results dealing with the weak approximation property of Banach spaces are considered for $p$-weak property. Also, an observation on bounded and $p$-bounded properties is given. Moreover, proof solution duality problem which exists in literature given a shorter way as alternative.