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Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups. (English) Zbl 0545.46051

Let M be a von Neumann algebra and A be a complex Banach space whose dual is M. Suppose there is a multiplication on A with respect to which the unit element of M becomes a multiplicative functional. Then the pair (A,M) is said to be an F-algebra. This abstract setting includes important specific Banach algebras appearing in harmonic analysis. The author provides a unified treatment of various characterizations of (one or two sided) amenability of A in terms of properties of M and of its dual.
Reviewer: J.Zemánek

MSC:

46L99 Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.)
22D15 Group algebras of locally compact groups
46H05 General theory of topological algebras
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