Functional calculus and *-regularity of a class of Banach algebras
Copyright policy )Functional calculus and *-regularity of a class of Banach algebras
Suppose that ( A , G , α ) (A,G,\alpha ) is a C ∗ C^* -dynamical system such that G G is of polynomial growth. If A A is finite dimensional, we show that any element in K ( G ; A ) K(G;A) has slow growth and that L 1 ( G , A ) L^1(G, A) is ∗ * -regular. Furthermore, if G G is discrete and π \pi is a “nice representation” of A A , we define a new Banach ∗ * -algebra l π 1 ( G , A ) l^1_{\pi }(G, A) which coincides with l 1 ( G ; A ) l^1(G;A) when A A is finite dimensional. We also show that any element in K ( G ; A ) K(G;A) has slow growth and l π 1 ( G , A ) l^1_{\pi }(G, A) is ∗ * -regular.
- Nankai University China (People's Republic of)
- The Chinese University of Hong Kong Hong Kong
- Chinese University of Hong Kong China (People's Republic of)
- The Chinese University of Hong-Kong Hong Kong
- Department of Mathematics, The Chinese University of Hong Kong Hong Kong
Functional calculus for linear operators, Polynomial growth, \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, Applied Mathematics, dynamical systems, functional calculus, Regularity, C∗-dynamical system, Banach algebras, General theory of topological algebras with involution, Noncommutative dynamical systems, Analysis, \(L^1\)-algebras on groups, semigroups, etc.
Functional calculus for linear operators, Polynomial growth, \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, Applied Mathematics, dynamical systems, functional calculus, Regularity, C∗-dynamical system, Banach algebras, General theory of topological algebras with involution, Noncommutative dynamical systems, Analysis, \(L^1\)-algebras on groups, semigroups, etc.
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