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II Congreso Iberoamericano de Topología y sus Aplicaciones
March 20-22, 1997

Morelía, Mexico

Organizers
Salvador García-Ferreira, Daniel Juan Pineda, Sergio Macías Alvarez, Max Neumann Coto, María L. Pérez Seguí, Salvador Romaguera Bonilla, Manuel Sanchis López, Angel Tamariz Mascarúa, M. G. Tkachenko, Javier F. Trigos Arrieta

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A characterization of the Schur property by means of the Bohr topology
by
Salvador Hernández
Universidad Jaume I
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: February 9, 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 # caak-17.