Pointwise amenability for dual Banach algebras. (English) Zbl 1405.46030

Shakeri, Mannane; Mahmoodi, Amin

Bull. Belg. Math. Soc. - Simon Stevin 25, No. 3, 393-401 (2018).

Dual Banach algebras have an important place in the theory of Banach algebras. V. Runde [Stud. Math. 148, No. 1, 47–66 (2001; Zbl 1003.46028)] defined the notion of Connes amenability for the category of dual Banach algebras. Ghahramani et al. [H. G. Dales and R. J. Loy, Diss. Math. 474, 58 p. (2010; Zbl 1245.46039)] introduced approximate notions of amenability. Following these two approaches, the authors define two concepts of pointwise and approximate \(w^*\)-pointwise Connes amenability for dual Banach algebras. They study some concrete dual Banach algebras like semigroup algebras and Banach sequence algebras under these new notions. They also investigate these notions through some diagonals.

Reviewer: Amir Sahami (Tehran)

MSC:

46H25	Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
16E40	(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
43A20	\(L^1\)-algebras on groups, semigroups, etc.

Keywords:

dual Banach algebras; Connes amenability; semigroup algebras; Banach sequence algebras

Citations:

Zbl 1003.46028; Zbl 1245.46039