Abstract
In this paper, we investigate the pseudo-amenability of semigroup algebra ℓ 1(S), where S is an inverse semigroup with uniformly locally finite idempotent set. In particular, we show that for a Brandt semigroup \(S={\mathcal{M}}^{0}(G,I)\), the pseudo-amenability of ℓ 1(S) is equivalent to the amenability of G.
Similar content being viewed by others
References
Choi, Y.: Biflatness of ℓ 1-semilattice algebras. Semigroup Forum 75, 253–271 (2007)
Choi, Y., Ghahramani, F., Zhang, Y.: Approximate and pseudo-amenability of various classes of Banach algebras. J. Funct. Anal. 256, 3158–3191 (2009)
Dales, H.G., Lau, A.T., Strauss, D.: Banach algebras on semigroups and their compactifications. Mem. Am. Math. Soc. 205, 1–165 (2010)
Esslamzadeh, G.H.: Double centralizer algebras of certain Banach algebras. Monatshette Math. 142, 193–203 (2004)
Ghahramani, F., Loy, R.J.: Generalized notions of amenability. J. Funct. Anal. 208, 229–260 (2004)
Ghahramani, F., Stokke, R.: Approximate and pseudo-amenability of the Fourier algebra. Indiana Univ. Math. J. 56(2), 909–930 (2007)
Ghahramani, F., Zhang, Y.: Pseudo-amenable and pseudo-contractible Banach algebras. Math. Proc. Camb. Philos. Soc. 142, 111–123 (2007)
Howie, J.: Fundamental of Semigroup Theory. London Math. Society Monographs, vol. 12. Clarendon Press, Oxford (1995)
Johnson, B.E.: Cohomology in Banach algebras. Mem. Am. Math. Soc. 127 (1972)
Johnson, B.E.: Approximate diagonals and cohomology of certain annihilator Banach algebras. Am. J. Math. 94, 685–698 (1972)
Johnson, B.E.: Symmetric amenability and the nonexistence of Lie and Jordan derivations. Math. Proc. Camb. Philos. Soc. 120, 455–473 (1996)
Ramsden, P.: Biflatness of semigroup algebras. Semigroup Forum 79, 515–530 (2009)
Sadr, M.M.: Pseudo-amenability of Brandt semigroup algebras. Comment. Math. Univ. Carol. 50(3), 413–419 (2009)
Sadr, M.M., Pourabbas, A.: Approximate amenability of Banach category algebras with application to semigroup algebras. Semigroup Forum 79, 55–64 (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Mohan S. Putcha.
Rights and permissions
About this article
Cite this article
Essmaili, M., Rostami, M. & Pourabbas, A. Pseudo-amenability of certain semigroup algebras. Semigroup Forum 82, 478–484 (2011). https://doi.org/10.1007/s00233-010-9278-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00233-010-9278-2