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A survey on the Szlenk index and some of its applications.

Gilles Lancien (2006)


We describe how the Szlenk index has been used in various areas of the geometry of Banach spaces. We cover the following domains of application of this notion: non existence of universal spaces, linear classification of C(K) spaces, descriptive set theory, renorming problems and non linear classification of Banach spaces.

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