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- W2091251104 abstract "Given a Banach algebra A, we introduce the notion of a left dual Banach algebra (LDBA) over A, and we establish that every LDBA over A is a left Arens product algebra over A. This can be viewed as a Banach algebraic version of the fact that every semigroup compactification is a Gelfand compactification. We show how A-module operations can be extended to obtain module operations for left Arens product algebras over A that satisfy attractive w*-continuity properties. We introduce a notion of left Connes amenability for LDBAs, and show that the amenability of a locally compact group G is equivalent to left Connes amenability of either the bidual L1(G)** of its group algebra L1(G), or the dual LUC(G)* where LUC(G) is the space of left uniformly continuous functions on G." @default.
- W2091251104 created "2016-06-24" @default.
- W2091251104 creator A5045467460 @default.
- W2091251104 date "2014-06-27" @default.
- W2091251104 modified "2023-09-27" @default.
- W2091251104 title "AMENABILITY AND MODULES FOR ARENS PRODUCT ALGEBRAS" @default.
- W2091251104 doi "https://doi.org/10.1093/qmath/hau018" @default.
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