On φ-Connes amenability of dual Banach algebras

Subject Areas : Functional analysis

A. Mahmoodi ^{1 *}

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

Received: 2014-09-29 Accepted : 2014-12-10 Published : 2014-12-01

Keywords: Dual Banach algebra, φ-Connes amenability, φ-injectivity,

Abstract :

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 typeof diagonal for dual Banach algebras is defined. It is proved that the existence of such a diagonal is equivalent to φ-Connes amenability. It is also shown that φ-Connes amenabilityis equivalent to so-called φ-splitting of a certain short exact sequence.

References:

[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.