AMENABILITY AND MODULES FOR ARENS PRODUCT ALGEBRAS
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Bibliographic record
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.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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