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Weak amenability of Banach algebras on locally compact groups. (English) Zbl 0890.46036

The paper is a contribution to the investigations concerning the implications of amenability for algebras over locally compact groups \(G\). This question is studied for \(M(G)\), the measure algebra of \(G\), for left inverted subspaces of \(L^\infty(G)\), especially spaces of almost periodic and weakly almost periodic functions, for \(L^1(G)\), and for the von Neumann algebra generated by the left regular representations of \(G\). The outcome is a series of results connecting – by necessary or sufficient conditions – weak amenability properties of these algebras and properties of \(G\) and its subgroups.
Reviewer: G.Garske (Hagen)

MSC:

46H05 General theory of topological algebras
22D15 Group algebras of locally compact groups
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