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Three-space problems in discrete spectra of C*-algebras and dual C*-algebras

Published online by Cambridge University Press:  12 July 2007

Masaharu Kusuda
Masaharu Kusuda
Affiliation:
Department of Mathematics, Faculty of Engineering, Kansai University, Suita, Osaka 564-8680, Japan (kusuda@ipcku.kansai-u.ac.jp)
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Abstract

We discuss the three-space problem on discreteness for the Jacobson topology on the spectrum of a C*-algebra in detail. As an application, it is shown that a C*-algebra A is a dual C*-algebra if and only if a closed ideal I of A and the quotient A/I are dual C*-algebras and the open central projection, in the second dual of A, corresponding to I is a multiplier for A.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 3 , June 2001 , pp. 701 - 707
Copyright
Copyright © Royal Society of Edinburgh 2001

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