Previous |  Up |  Next

Article

Keywords:
pseudo-amenability; Brandt semigroup algebra; amenable group
Summary:
In this paper it is shown that for a Brandt semigroup $S$ over a group $G$ with an arbitrary index set $I$, if $G$ is amenable, then the Banach semigroup algebra $\ell^1(S)$ is pseudo-amenable.
References:
[1] Duncan J., Namioka I.: Amenability of inverse semigroups and their semigroup algebras. Proc. Royal Soc. Edinburgh Sect. A 80 (1978), 309--321. MR 0516230 | Zbl 0393.22004
[2] Ghahramani F., Loy R.J.: Generalized notion of amenability. J. Funct. Anal. 208 (2004), 229--260. DOI 10.1016/S0022-1236(03)00214-3 | MR 2034298
[3] Ghahramani F., Loy R.J., Zhang Y.: Generalized notions of amenability II. J. Funct. Anal. 254 (2008), 1776--1810. DOI 10.1016/j.jfa.2007.12.011 | MR 2397875 | Zbl 1146.46023
[4] Ghahramani F., Zhang Y.: Pseudo-amenable and pseudo-contractible Banach algebras. Math. Proc. Cambridge Philos. Soc. 142 (2007), 111--123. DOI 10.1017/S0305004106009649 | MR 2296395 | Zbl 1118.46046
[5] Howie J.M.: An Introduction to Semigroup Theory. Academic Press, London, 1976. MR 0466355 | Zbl 0355.20056
[6] Johnson B.E.: Cohomology in Banach algebras. Mem. Amer. Math. Soc. 127 (1972), pp 96. MR 0374934 | Zbl 0306.46065
[7] Lashkarizadeh Bami M., Samea H.: Approximate amenability of certain semigroup algebras. Semigroup Forum 71 (2005), 312--322. DOI 10.1007/s00233-005-0516-y | MR 2184061 | Zbl 1086.43002
[8] Runde V.: Lectures on amenability. Lecture Notes in Mathematics, 1774, Springer, Berlin, 2002. DOI 10.1007/b82937 | MR 1874893 | Zbl 0999.46022
[9] Sadr M.M., Pourabbas A.: Approximate amenability of Banach category algebras with application to semigroup algebras. Semigroup Forum(to appear). MR 2534223
Partner of
EuDML logo