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Character Connes amenability of dual Banach algebras. (English) Zbl 06861578
Summary: We study the notion of character Connes amenability of dual Banach algebras and show that if $$A$$ is an Arens regular Banach algebra, then $$A^{**}$$ is character Connes amenable if and only if $$A$$ is character amenable, which will resolve positively Runde’s problem for this concept of amenability. We then characterize character Connes amenability of various dual Banach algebras related to locally compact groups. We also investigate character Connes amenability of Lau product and module extension of Banach algebras. These help us to give examples of dual Banach algebras which are not Connes amenable.

##### MSC:
 46H20 Structure, classification of topological algebras 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 43A07 Means on groups, semigroups, etc.; amenable groups 22D15 Group algebras of locally compact groups
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