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Gâteaux differentiability of convex functions and topology : weak asplund spaces

TLDR
In this article, a characterisation of WCG Spaces and of Eberlein Compacta is presented, and two concrete classes of Banach Spaces that lie in. Fragmentability.
Abstract
Canonical Examples of Weak Asplund Spaces. Properties of Gateaux Differentiability Spaces and Weak Asplund Spaces. Stegall's Classes. Two More Concrete Classes of Banach Spaces that Lie in . Fragmentability. "Long Sequences" of Linear Projections. Vasak Spaces and Gul'ko Compacta. A Characterization of WCG Spaces and of Eberlein Compacta. Main Open Questions and Problems. References. Index.

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Functional Analysis and Infinite-Dimensional Geometry

TL;DR: In this article, the basic concepts in Banach spaces are discussed, including weak topologies, uniform convexity, smoothness and structure, and weakly compactly generated spaces.
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Convex Functions: Constructions, Characterizations and Counterexamples

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Hereditarily non-sensitive dynamical systems and linear representations

TL;DR: In this article, the Radon-Nikodým system (RN) is defined as a compact G-dynamical system which can be represented as a weak ∗-compact subset of a dual Banach space with the radon-nikodþm property.
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Enveloping semigroups in topological dynamics

TL;DR: A survey of the theory of enveloping semigroups in topological dynamics can be found in this paper, where the authors review the existing classical theory of envelope groups, due mainly to Robert Ellis, and then proceed to describe some new connections which were discovered in the last few years between three seemingly unrelated theories: enveloping semiigroups, chaotic behavior, and representation of dynamical systems on Banach spaces.
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Essentially Smooth Lipschitz Functions

TL;DR: In this paper, the authors examined the relationship between integrability, D-representability, and strict differentiability of locally Lipschitz functions on separable Banach spaces.