Reflexivity of Cyclic Banach Spaces

Poisson’s equation and characterizations of reflexivity of Banach spaces

A Geometrical Characterization of Reflexivity in Banach Spaces

Duality, Reflexivity and Atomic Decompositions in Banach Spaces

We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of “shrinking” and “boundedly complete” Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. ...

Metrical Characterization of Super-reflexivity and Linear Type of Banach Spaces

We prove that a Banach space X is not super-reflexive if and only if the hyperbolic infinite tree embeds metrically into X. We improve one implication of J.Bourgain’s result who gave a metrical characterization of super-reflexivity in Banach spaces in terms of uniforms embeddings of the finite trees. A characterization of the linear type for Banach spaces is given using the embedding of the inf...

Multi - Dimensional Volumes , Super - Reflexivity and Normal Structure in Banach Spaces

The notion of the n-dimensional volume enclosed by n + vectors in a Banaeh space, E, was introduced by Silverman [12], and some of the connections between higher dimensional volumes and geometric properties of E were studied in [13] and [6]. In particular, it was shown that a kuniformly rotund Banach space is super-reflexive and has normal structure. (Definitions are given below.) The present p...