Document Type: Research Paper

Authors

Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

Abstract

In this paper,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $\ell^1(S,\omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $\ell^1(G,\omega)$ are the same. Examples are given to show that the class of $\sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.

Keywords

Main Subjects

###### ##### References

[1] H.G. Dales, Banach algebras and automatic continuity, Clarendon Press, Oxford, 2000.

[2] H.G. Dales and A. T.-M. Lau, The second duals of Beurling algebras, American Mathematical Society, 2005, no 836.

[3] M. Daws, Connes-amenability of bidual and weighted semigroup algebras, Math. Scand., 99 (2006), pp. 217-246.

[4] G.H. Esslamzadeh, B. Shojaee, and A. Mahmoodi, Approximate Connes-amenability of dual Banach algebras, Bull. Belgian Math. Soc. Simon Stevin, 19 (2012), pp. 193-213.

[5] F. Ghahramani and R.J. Loy, Generalized notions of amenability, J. Funct. Anal., 208 (2004), pp. 229-260.

[6] F. Ghahramani, R.J. Loy, and Y. Zhang, Generalized notions of amenability, II, J. Funct. Anal., 254 (2008), pp. 1776-1810.

[7] F. Ghahramani and Y. Zhang, Pseudo-amenable and pseudo-contractible Banach algebras, Math. Proc. Camb. Phil. Soc., 142 (2007), pp. 111-123.

[8] B. E. Johnson, Approximate diagonals and cohomology of certain annihilator Banach algebras, Amer. J. Math., 94 (1972), pp. 685-698.

[9] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 127 (1972), pp. 1-96.

[10] A. Mahmoodi, Approximate injectivity of dual Banach algebras, Bull. Belgian Math. Soc. Simon Stevin., 20 (2013), pp. 1-12.

[11] A. Mahmoodi, Bounded approximate Connes-amenability of dual Banach algebras, Bull. Iranian Math. Soc., 41 (2015), pp. 227-238.

[12] A. Mahmoodi, Connes-amenability-like properties, Studia Math., 220 (2014), pp. 55-72.

[13] M. Mirzavaziri and M. S. Moslehian, $sigma$-amenability of Banach algebras, Southeast Asian Bull. Math., 33 (2009), pp. 89-99.

[14] M. Mirzavaziri and M. S. Moslehian, $sigma$-derivation in Banach algebras, Bull. Iranian Math. Soc., 32 (2006), pp. 65-78.

[15] M.S. Moslehian and M.N. Motlagh, Some notes on $(sigma, tau)$-amenableof Banach algebras, Stud. Univ. Babe-s-Bolyai Math., 53 (2008), pp. 57-68.

[16] V. Runde, Amenability for dual Banach algebras, Studia Math., 148 (2001), pp. 47-66.

[17] V. Runde, Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule, Math. Scand., 95 (2004), pp. 124-144.

[18] V. Runde, Lectures on amenability, Lecture Notes in Mathematics 1774, Springer Verlag, Berlin, 2002.