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Journal of Operator Theory

Volume 63, Issue 2, Spring 2010  pp. 417-424.

A characterization of scattered C-algebras and its applications to C-crossed products

Authors Masaharu Kusuda
Author institution: Department of Mathematics, Faculty of Engineering Science, Kansai University, Yamate-cho 3-3-35, Suita, Osaka 564-8680, Japan

Summary:  It is well known that any scattered C-algebra is of type I and AF. We give conditions for C-algebras being of type I or AF to be scattered. In particular, it is shown that a C-algebra A is scattered if and only if A is a type~I C-algebra satisfying that the center of A is scattered. As an application to a C-dynamical system (A,G,α) with a compact abelian group G, it is shown that the fixed point algebra Aα of A under the action α is scattered if and only if so is the C-crossed product A×αG.


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