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Ideal Connes-amenability of dual Banach algebras. (English) Zbl 1385.46033
Summary: Following V. Runde [Stud. Math. 148, No. 1, 47–66 (2001; Zbl 1003.46028)], we define the concept of ideal Connes-amenability for dual Banach algebras. For an Arens regular dual Banach algebra \({\mathcal {A}}\), we prove that the ideal Connes-amenability of \(\mathcal {A^{**}}\), the second dual of \({\mathcal {A}}\), necessities ideal Connes-amenability of \({{\mathcal {A}}}\). As a typical example, we show that von Neumann algebras are always ideally Connes-amenable. For a locally compact group \(G\), the Fourier-Stieltjes algebra of \(G\) is ideally Connes-amenable, but not ideally 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
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