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Approximate Connes-amenability of dual Banach algebras. (English) Zbl 1254.46052

This paper is concerned with an approximate version of the so-called Connes amenability of dual Banach algebras. The authors study this concept for von Neumann algebras, measure algebras, and algebras of pseudomeasures. It is shown that a von Neumann algebra is approximately Connes amenable if and only if it has an approximate normal virtual diagonal. The measure algebra corresponding to a locally compact group is approximately Connes amenable if and only if it is Connes amenable.

MSC:

46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46H20 Structure, classification of topological algebras
46H35 Topological algebras of operators
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