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A NOTE ON IDEAL SPACES OF BANACH ALGEBRAS

Published online by Cambridge University Press:  01 November 1998

J. F. FEINSTEIN  and
D. W. B. SOMERSET
J. F. FEINSTEIN
Affiliation:
Department of Mathematics, University of Nottingham, Nottingham NG7 2RD
D. W. B. SOMERSET
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE
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Abstract

In a previous paper, the second author introduced a compact topology τr on the space of closed ideals of a unital Banach algebra A. If A is separable, then τr is either metrizable or else neither Hausdorff nor first countable. Here it is shown that τr is Hausdorff if A is C1[0, 1], but that if A is a uniform algebra, then τr is Hausdorff if and only if A has spectral synthesis. An example is given of a strongly regular, uniform algebra for which every maximal ideal has a bounded approximate identity, but which does not have spectral synthesis.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 6 , November 1998 , pp. 611 - 617
Copyright
© The London Mathematical Society 1998

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