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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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On (BB)n properties on Fréchet spaces
by
José M. Ansemil
Universidad Complutense de Madrid
Coauthors: Fernando Blasco (Universidad Politécnica de Madrid), Socorro Ponte (Universidad Complutense de Madrid)

Properties (BB)n on a locally convex space have been introduced by Dineen as a generalization of the (BB) property defined by Taskinen in relation with the ''problème des topologies'' of Grothendieck, and have been considered by several authors: Defant-Maestre, Díaz, Dineen, Galindo-García-Maestre... We say that a locally convex space E has the (BB)n property (for a given natural number n greater or equal to 2) if for every bounded subset B in the n-fold projective complete tensor product of E by itself n times, there is a bounded subset C in E such that B is contained in the closed convex hull of the tensor product of C by itself n times.

While it is known that for a given n >= 3, the (BB)n property implies the (BB)n-1 property, there are no examples in the literature of locally convex spaces E with property (BB)n-1 but without property (BB)n. In this talk a recent result by Blasco, Ponte and myself giving an example of a Fréchet space E with property (BB)2, but without property (BB)3, is presented.

(T)

Date received: April 3, 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-63.