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


Let φ be a w-continuous homomorphism from a dual Banach algebra to C. The notion of φ-Connes amenability is studied and some characterizations is given. A type of diagonal for dual Banach algebras is de ned. It is proved that the existence of such a diagonal is equivalent to φ-Connes amenability. It is also shown that φ-Connes amenability is equivalent to so-called φ-splitting of a certain short exact sequence.


Main Subjects

[1] H. G. Dales, Banach algebras and automatic continuity, Clarendon Press, Oxford, 2000.
[2] M. Daws, Connes-amenability of bidual and weighted semigroup algebras, Math. Scand. 99 (2006), 217-246.
[3] M. Daws, Dual Banach algebras: representations and injectivity, Studia Math. 178 (2007), 231-275.
[4] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972).
[5] E. Kaniuth, A. T. Lau, J. Pym, On φ-amenability of Banach algebras, Math. Proc. Camb. Phil. Soc. 144 (2008), 85-96.
[6] M. S. Monfared, Character amenability of Banach algebras, Math. Proc. Camb. Phil. Soc. 144 (2008), 697-706.
[7] V. Runde, Amenability for dual Banach algebras, Studia Math. 148 (2001), 47-66.
[8] V. Runde, Lectures on amenability, Lecture Notes in Mathematics 1774, Springer Verlag, Berlin, 2002.
[9] V. Runde, Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule, Math. Scand. 95 (2004), 124-144.