Journal of Operator Theory
Volume 49, Issue 1, Winter 2003 pp. 173-183.
C∗-crossed products of C∗-algebras with the weak Banach-Saks propertyAuthors: Masaharu Kusuda
Author institution: Department of Mathematics, Faculty of Engineering, Kansai University, Yamate-Cho 3-3-35, Suita,Osaka 564-8680, Japan
Summary: Let (A,G,α) be a C∗-dynamical system. In Section 2, we first treat the discrete group action case. We suppose that G acts freely on the spectrum of A. Then it is shown that A has the weak Banach-Saks property, if and only if G is discrete and the C∗-crossed product A×αG has the weak Banach-Saks property. In Section 3, we shall consider the compact group action case. Let G be a compact group and consider the following conditions 1--3: 1 A has the weak Banach-Saks property; 2 A×αG has the weak Banach-Saks property; 3 the fixed point algebra Aα of A has the weak Banach-Saks property. Then it is shown that we have 1 ⟹ 2 ⟹ 3. Furthermore we suppose that G is compact abelian. Then it is shown that the implication 3 ⟹ 2 holds, and that if A is of type I and if α is pointwise unitary, the implication 2 ⟹ 1 holds.
Keywords: C∗-crossed product, weak Banach-Saks property, C∗-dynamical system
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