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Generalized notions of amenability. II. (English) Zbl 1146.46023

J. Funct. Anal. 254, No. 7, 1776-1810 (2008); corrigendum ibid. 278, No. 6, Article ID 108406, 11 p. (2020).
In Part I [J. Funct. Anal. 208, No. 1, 229–260 (2004; Zbl 1045.46029)], the first two authors introduced certain notions of amenability for Banach algebras that generalize B. E. Johnson’s definition of an amenable Banach algebra [“Cohomology in Banach algebras.” Mem. Am. Math. Soc. 127 (1972; Zbl 0256.18014)].
In the paper under review, the authors continue the study of generalized notions of amenability. Further such generalizations are introduced and investigated. The rôle of approximate identities (not necessarily bounded) is highlighted.
The paper concludes with a new proof of a result by N. Grønbæk characterizing the amenable Beurling algebras, i.e., weighted \(L^1\)-algebras, on locally compact groups [Trans. Am. Math. Soc. 319, No. 2, 765–775 (1990; Zbl 0701.46035)].
Editor’s remark: A corrigendum has been published in [J. Funct. Anal. 278, No. 6, Article ID 108406, 11 p. (2020; Zbl 1446.46033)].

MSC:

46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46H05 General theory of topological algebras
43A20 \(L^1\)-algebras on groups, semigroups, etc.
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