*-regularity of certain generalized group algebras
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AbstractLet B be a *-semisimple Banach algebra with a bounded approximate identity and alpha : G -> Aut(*)(B) (isometric *-automorphisms group of B) an action of a locally group G on B. Let (D, G, gamma) be the associated dynamical system, where D = C-0(G, B) is the Banach *-algebra of all continuous B-valued functions on G vanishing at infinity and the action gamma : G -> Aut D is given by gamma(s)(y)(t) = alpha(s)(y(s(-1) t)) for y is an element of D and s, t is an element of G. Recall that B is said to be *-regular if the natural mapping I is an element of Prim C*(B) bar right arrow I boolean AND B. Prim(*)(B) is a homeomorphism under the hull-kernel topology. When G is amenable, we show that if B is *-regular, then the generalized group algebra L-1 (G, D; gamma) is *-regular. The converse is also true if we further assume that G is countable discrete. Finally the case of compact groups is studied.
All Author(s) ListLeung CW
Journal nameArchiv der Mathematik
Year2011
Month5
Day1
Volume Number96
Issue Number5
PublisherSpringer Verlag (Germany)
Pages445 - 454
ISSN0003-889X
LanguagesEnglish-United Kingdom
Keywords*-regular Banach algebras; Amenable groups; Generalized group algebras
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2021-14-01 at 23:42