### Approximate Connes-amenability of dual Banach algebras

G. H. Esslamzadeh, B. Shojaee, and A. Mahmoodi
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 19, Number 2 (2012), 193-213.

#### 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.

First Page:
Primary Subjects: 46H25, 46H20
Secondary Subjects: 46H35
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Permanent link to this document: http://projecteuclid.org/euclid.bbms/1337864267
Zentralblatt MATH identifier: 06050933
Mathematical Reviews number (MathSciNet): MR2977226