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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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The Szlenk index and its applications
by
Gilles Godefroy
Paris VI, France

The Szlenk derivation consists of removing from the dual unit ball of a Banach space X the weak-star open sets which have a small diameter in norm, and iterating the operation. The Szlenk index (which is a well-defined ordinal number when X is an Asplund space) is obtained by counting how many steps are needed for reaching the empty set. We will survey various applications of this notion: renormings, coanalytic non-Borel families of Banach spaces, Lipschitz and uniform classification of separable Banach spaces. Several open problems will be mentioned.

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Date received: April 11, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caei-99.