Ghahramani, F.; Lau, A. T. M. Weak amenability of certain classes of Banach algebras without bounded approximate identities. (English) Zbl 1010.46048 Math. Proc. Camb. Philos. Soc. 133, No. 2, 357-371 (2002). A Banach algebra \(A\) is called weakly amenable if each continuous derivation from \(A\) into the dual space \(A^*\) treated as an \(A\)-bimodule is an inner one. Here the authors deal with weak amenability of various types of Segal algebras. Among other results, they show that every Segal algebra on a locally compact abelian group is weakly amenable and that an abstract Segal sub-algebra (with an approximate identity) of a commutative weakly amenable Banach algebra is weakly amenable. They also introduce the Lebesgue-Fourier algebra of a locally compact group and obtain several results concerning Arens regularity, derivations and multipliers. Reviewer: Wiesław Tadeusz Zelazko (Warszawa) Cited in 2 ReviewsCited in 22 Documents MSC: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc. 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc. Keywords:amenabiltity; Arens regularity; derivations PDFBibTeX XMLCite \textit{F. Ghahramani} and \textit{A. T. M. Lau}, Math. Proc. Camb. Philos. Soc. 133, No. 2, 357--371 (2002; Zbl 1010.46048) Full Text: DOI