Module Amenability of module dual Banach algebras

Subject Areas : Statistics

M.  Khoshhal ¹ (Department of Mathematics, Faculty of Basic Science, Islamic Azad University, ‍Centeral Tehran Branch, Tehran, Iran)
D.  Ebrahimi Bagha ² (Department of Mathematic, Faculty of Basic Science, Islamic Azad University, Centeral Tehran Branch,Tehran, Iran)
O.  pourbahri rahpeyma ³ (Department of Mathematic, Islamic Azad University, Chalous Branch,Chalous, Iran)

Received: 2018-06-28 Accepted : 2019-10-11 Published : 2020-01-21

Keywords: میانگین پذیری مدولی, توابع متناوب ضعیف مدولی, –σWC قطر حقیقی مدولی, کن – میانگین پذیری مدولی, جبر باناخ دوگان مدولی,

Abstract :

In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe relation between module amenability, weak module amenability and module approximate amenability of Banach algebra. The notation of amenability of Banach algebras was introduced by B.Johnsonin [7]. A Banach algebra A is amenable if every bounded derivation from Ainto any dual Banach A-bimodule is inner, equivalently if H(A;X) = 0 for any Banach A-bimodule X, where H(A;X) is the first Hochschild co-homology group of A with coefficient in X. Also, a Banach algebra A isweakly amenable if H(A;A) = 0. Bade, Curtis and Dales introduced the notion of weak amenability on Banach algebras in [4]. They considered this concept only for commutative Banach algebras. After that Johnson defined the weak amenability for arbitrary Banach algebras.

References:

 

[1] M. Amini, ”Module arens regularity for semigroup algebras,”Semigroupfourm, 77, (2008), 300-305.

 

[2] M. Amini, “Module amenability for semigroup algebras,” Semigroupfourm, 69, (2004), 302 – 312.

 

[3] J. B. Conway, “A course in functional Analysis”, Springer –Verlag, New York, 1985.

 

[4] H. G. Dales, “Banach algebras and automatic continuity,” Clarendon, Oxford, (2000).

 

[5] V. Runde, ”Lectures on amenability,” Lecturer Notes in mathematics 1774, Springer- Verlage, Berlin, 2002.

 

[6] V. Runde,” Amenability for dual Banachalgebras”, Studia  Math. 148, (2001), 47-66.

 

[7] V.Runde,”Dual Banach algebras: Connes-amenability, normal, virtual diagonals , and ingectivity of the redualbimodule”, Math.SCAND. 95(2004), 124-144.

 

[8] T. W. Palmer, “Banach algebras and the general theory of *-algebras,” Volume 1, Cambridge University press, (1994).