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march 2012 Approximate Connes-amenability of dual Banach algebras
G. H. Esslamzadeh, B. Shojaee, A. Mahmoodi
Bull. Belg. Math. Soc. Simon Stevin 19(2): 193-213 (march 2012). DOI: 10.36045/bbms/1337864267

Abstract

We introduce the notions of approximate Connes-amenability and approximate strong Connes-amenability for dual Banach algebras. Then we characterize these two types of algebras in terms of approximate normal virtual diagonals and approximate $\sigma WC-$virtual diagonals. We investigate these properties for von Neumann algebras, measure algebra and the algebra of $p$-pseudomeasures on locally compact groups. In particular we show that a von Neumann algebra is approximately Connes-amenable if and only if it has an approximate normal virtual diagonal. This is the ``approximate'' analog of the main result of Effros in [10]. We show that in general the concepts of approximate Connes-amenability and Connes-amenability are distinct, but for measure algebras these two concepts coincide. Moreover cases where approximate Connes-amenability of $\mathcal{A}^{**}$ implies approximate Connes-amenability or approximate amenability of $\mathcal{A}$ are also discussed.

Citation

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G. H. Esslamzadeh. B. Shojaee. A. Mahmoodi. "Approximate Connes-amenability of dual Banach algebras." Bull. Belg. Math. Soc. Simon Stevin 19 (2) 193 - 213, march 2012. https://doi.org/10.36045/bbms/1337864267

Information

Published: march 2012
First available in Project Euclid: 24 May 2012

zbMATH: 1254.46052
MathSciNet: MR2977226
Digital Object Identifier: 10.36045/bbms/1337864267

Subjects:
Primary: 46H20, 46H25
Secondary: 46H35

Rights: Copyright © 2012 The Belgian Mathematical Society

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Vol.19 • No. 2 • march 2012
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