Topologies on the ideal space

of a Banach algebra and spectral synthesis

Author:
Ferdinand Beckhoff

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2859-2866

MSC (1991):
Primary 46J20

DOI:
https://doi.org/10.1090/S0002-9939-97-03831-8

MathSciNet review:
1389504

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Abstract | References | Similar Articles | Additional Information

Abstract: Let the space of closed two-sided ideals of a Banach algebra carry the weak topology. We consider the following property called normality (of the family of finite subsets of : if the net in converges weakly to , then for all we have (e.g. -algebras, with compact . For a commutative Banach algebra normality is implied by spectral synthesis of all closed subsets of the Gelfand space , the converse does not always hold, but it does under the following additional geometrical assumption: .

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Additional Information

**Ferdinand Beckhoff**

Affiliation:
Mathematisches Institut der Universität Münster, Einsteinstraße 62, 48149 Münster, Germany

Email:
beckhof@math.uni-muenster.de

DOI:
https://doi.org/10.1090/S0002-9939-97-03831-8

Received by editor(s):
October 3, 1995

Received by editor(s) in revised form:
March 19, 1996

Communicated by:
Theodore Gamelin

Article copyright:
© Copyright 1997
American Mathematical Society