Geometry of Banach Spaces: A New Route Towards Position Based Cryptography

A New Class of Banach Sequence Spaces

The Nonlinear Geometry of Banach Spaces

We survey some of the recent developments in the nonlinear theory of Banach spaces, with emphasis on problems of Lipschitz and uniform homeomorphism and uniform and coarse embeddings of metric spaces.

The Geometry of Convex Transitive Banach Spaces

Throughout this paper, X will denote a Banach space, S ̄S(X ) and B ̄B(X ) will be the unit sphere and the closed unit ball of X, respectively, and ' ̄'(X ) will stand for the group of all surjective linear isometries on X. Unless explicitly stated otherwise, all Banach spaces will be assumed to be real. Nevertheless, by passing to real structures, the results remain true for complex spaces. Recal...

Randomized Series and Geometry of Banach Spaces

Abstract. We study some properties of the randomized series and their applications to the geometric structure of Banach spaces. For n ≥ 2 and 1 < p < ∞, it is shown that l ∞ is representable in a Banach space X if and only if it is representable in the Lebesgue-Bochner Lp(X). New criteria for various convexity properties in Banach spaces are also studied. It is proved that a Banach lattice E is...

The Geometry of Banach Spaces. Smoothnesso'2)

Introduction. This paper contains the first unified treatment of the dual theory of differentiability of the norm functional in a real normed linear space. With this, the work of Smulian [2; 3] is extended and it is shown how uniform convexity is to be modified so as to obtain geometric properties dual to the various types of differentiability of the norm thus answering a question implicit in t...