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three space problem

Proceedings of the London Mathematical Society (1)

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Locally uniformly rotund renorming and fragmentability
A Moltó, J Orihuela, S Troyanski
Journal:

Proceedings of the London Mathematical Society / Volume 75 / Issue 3 / November 1997

Published online by Cambridge University Press:

01 November 1997, pp. 619-640

Print publication:

November 1997
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In this paper we characterize those Banach spaces $E$ that admit a locally uniformly rotund renorming by means of a linear topological condition that is a particular case of the notion, introduced by J. E. Jayne, I. Namioka and C. A. Rogers, called countable cover by sets of small local diameter. This allows us to develop a Decomposition Method and a Transfer Technique to obtain locally uniformly rotund renormings.
1991 Mathematics Subject Classification: 46B20.