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The 1997 Spring Topology and Dynamics Conference
April 10-12, 1997
University of Southwestern Louisiana
Lafayette, LA, USA

Organizers
Bradd Clark, Kathleen Lopez, Vic Schneider, Roger Waggoner, Thelma West

View Abstracts

A characterization of the Schur property by means of the Bohr topology
by
Salvador Hernández
Departamento de Matemáticas, Universitat Jaume I, Campus de Penyeta Roja, 12071-Castellón (Spain)
Coauthors: Jorge Galindo, Sergio Macario

Let G be a MAPA group that is metrizable and satisfies Pontryagin duality, that is, coincides with its topological bidual. We prove that the Bohr topology of G respects compactness if and only if every non-totally bounded subset contains an infinite discrete subset which is C*-embedded in its Bohr compactification. This result is used to characterize the Banach spaces which respect compactness (or have the Schur property, using a different terminology). Among other equivalent properties, we prove that a Banach space E has the Schur property if and only if every bounded basic sequence contains an infinite subsequence equivalent to a l1 basis.

Date received: March 5, 1997

Copyright © 1997 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 # caam-46.