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Set Theory, Topology and Banach Spaces (Second International Topology Conference in Kielce)
July 7-11, 2008
Institute of Mathematics, Jan Kochanowski University in Kielce; co-organized by Technical University of Lodz
Kielce, Poland |
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Organizers
Taras Banakh, Piotr Koszmider, Wieslaw Kubis
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A spectral synthesis property for Cb( X, b)
by
Hugo Arizmendi Peimbert
Universidad Nacional Autónoma de México
Coauthors: Ángel Carrillo, Armando García
Abstract
Let ( Cb( X) , b) be the algebra of all
continuous bounded real or complex valued functions defined on a completely
regular Hausdorff space X with the usual algebraic operations and with the
strict topology b. It is proved that ( Cb( X), b) has a spectral synthesis, i.e. every of its
closed ideals is an intersection of closed maximal ideals of codimension 1.
We give one necessary and two sufficient conditions over X in order that ( Cb( X) , b) has no proper non-zero closed
principal ideals. Moreover if X satisfy any of these two conditions and is
also a k-space, then any non zero element of Cb( X) is
invertible or a topological divisor of zero.
2000 Mathematics Subject Classification: 46J05 (46J20).
Keywords and phrases: spectral synthesis, strict
topology, closed ideals, topological divisors of zero.
Date received: June 24, 2008
Copyright © 2008 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 # caxg-20.