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 productsAuthors: 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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