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The 12th Summer Conference on General Topology and its Applications
August 12-16, 1997
Nipissing University
North Bay, ON, Canada

Organizers
Ted Chase, Boguslaw Schreyer, Jodi Sutherland, Murat Tuncali, Stephen Watson

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Ideal Spaces of Banach Algebras
by
D. Somerset
University of Aberdeen, United Kingdom

Let A be a Banach algebra and let Id(A) be the space of closed, two-sided ideals of A. We study Id(A) as a bitopological space (Id(A), \tauu, \taun), where \tauu is the weakest topology for which all the norm functions I --> ||a + I|| (a in A, I in Id(A)) are upper semi-continuous, and \taun is the de Groot dual of \tauu. When A is separable a dichotomy occurs: either \taun \/ \tauu is a compact, metrizable topology, or it is not first countable.

In the most favourable case (which includes C*-algebras, TAF-algebras, and Banach algebras with spectral synthesis) Id(A) is a continuous lattice and \taun \/ \tauu is the Lawson topology.

Date received: May 20, 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 # caao-10.