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Real group algebras. (English) Zbl 1074.43002

Authors’ abstract: We initiate the study of real group algebras and investigate some of its aspects. Let \(L^1(G)\) be a group algebra of a locally compact group \(G\), \(\tau:\;G\to G\) be a group homeomorphism such that \(\tau^2=\tau\circ\tau=1\), the identity map, and \(L^p(G,\tau)=\{f\in L^p(G):\;f\circ\tau=f\}\) (\(p\geq 1\)). Among other results, we clarify the structure of \(L^p(G,\tau)\) and characterize the amenability of \(L^1(G,\tau)\) and identify its multipliers.
Reviewer: Yang Dachun (Kiel)

MSC:

43A20 \(L^1\)-algebras on groups, semigroups, etc.
46J99 Commutative Banach algebras and commutative topological algebras
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