Abstract
In this paper we introduce the notion of module character amenable Banach algebras and show that they possess module character virtual (approximate) diagonals. As a basic example, we show that for an inverse semigroup S with the set of idempotents E, the semigroup algebra ℓ 1(S) is module character amenable as an ℓ 1(E)-module if only if S is amenable.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Amini M.: Module amenability for semigroup algebras. Semigroup Forum 69, 243–254 (2004)
Amini M., Bodaghi A., Ebrahimi Bagha D.: Module amenability of the second dual and module topological center of semigroup algebras. Semigroup Forum 80, 302–312 (2010)
Bodaghi A.: Module \({(\varphi, \psi)}\) -amenability of Banach algebras. Archivum Mathematicum. 46, 227–235 (2010)
Duncan J., Namioka I.: Amenability of inverse semigroups and their semigroup algebras. Proc. Roy. Soc. Edinburgh 80A, 309–321 (1988)
Howie J. M.: An Introduction to Semigroup Theory. Academic Press, London (1976)
Hu Z., Monfared M. S., Traynor T.: On character amenable Banach algebras. Studia Math. 193, 53–78 (2009)
B. E. Johnson Cohomology in Banach algebras, Memoirs Amer. Math. Soc. 127, Providence. 1972.
Kaniuth E., Lau A. T-M., Pym J.: On \({\varphi}\) -amenability of Banach algebras. Math. Proc. Camb. Soc. 144, 85–96 (2008)
Kaniuth E., Lau A. T-M., Pym J.: On character amenability of Banach algebras. J. Math. Anal. Appl. 344, 942–955 (2008)
Lau A. T-M.: Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups. Fund. Math. 118, 161–175 (1983)
Lau A.T-M., Ludwig J.: Fourier-Stieltjes algebra of a topological group. Adv. Math. 229, 2000–2023 (2012)
Monfared M. S.: Character amenability of Banach algebras. Math. Proc. Camb. Soc. 144, 697–706 (2008)
Munn W.D.: A class of irreducible matrix representations of an arbitrary inverse semigroup. Proc. Glasgow Math. Assoc. 5, 41–48 (1961)
Pourmahmood-Aghababa H.: (Super) Module amenability, module topological center and semigroup algebras. Semigroup Forum 81, 344–356 (2010)
Pourmahmood-Aghababa H.: A note on two equivalence relations on inverse semigroups. Semigroup Forum 84, 200–202 (2012)
Rezavand R. et al.: Module Arens regularity for semigroup algebras. Semigroup Forum 77, 300–305 (2008)
Šemrl P.: Additive derivations of some operator algebras. Illinois J. Math. 35, 234–240 (1991)
Author information
Authors and Affiliations
Corresponding author
Additional information
M. Amini was partly supported by a grant from IPM (No. 90430215).
Rights and permissions
About this article
Cite this article
Bodaghi, A., Amini, M. Module character amenability of Banach algebras. Arch. Math. 99, 353–365 (2012). https://doi.org/10.1007/s00013-012-0430-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-012-0430-y