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Abstract We prove that if X is a Banach space which admits a smooth Lipschitzian bump function, then for every lower semicontinuous bounded below function ƒ, there exists a Lipschitzian smooth… (More)
The main theme of this book is the relation between the global structure of Banach spaces and the various types of generalized "coordinate systems" - or "bases" - they possess. This subject is not… (More)
Preface * 1 Basic Concepts in Banach Spaces * 2 Hahn-Banach and Banach Open Mapping Theorems * 3 Weak Topologies * 4 Locally Convex Spaces * 5 Structure of Banach Spaces * 6 Schauder Bases * 7… (More)
and call r(x) the farthest distance from x to C. Equivalently, r(x) is the radius of the smallest ball of centre x , containing C. The function r is convex as supremum of such functions, and… (More)
A quantitative version of Krein's Theorem on convex hulls of weak compact sets is proved. Some applications to weakly compactly gen- erated Banach spaces are given.
It is shown that a Banach spaceX admits an equivalent uniformly Gâteaux smooth norm if and only if the dual ball ofX* in its weak star topology is a uniform Eberlein compact.