Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

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

Masaharu Kusudaa1

a1 Department of Mathematics, Faculty of Engineering, Kansai University, Suita, Osaka 564-8680, Japan (kusuda@ipcku.kansai-u.ac.jp)

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.

(Received October 04 1999)

(Accepted May 18 2000)