# \varphi-amenability of Banach algebras

Document Type : Research Paper

Authors

Semnan University

Abstract

Let $A$ be an arbitrary Banach algebra and $varphi$ a homomorphism from $A$ onto $Bbb C$. Our first purpose in this paper is to give some equivalent conditions under which
guarantees a $varphi$-mean of norm one. Then we find some conditions under which there exists a $varphi$-mean in the weak$^*$ cluster of ${ain A; |a|=varphi(a)=1}$ in $A^{**}$.

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### History

• Receive Date: 06 November 2010
• Revise Date: 09 April 2011
• Accept Date: 09 April 2011
• First Publish Date: 15 September 2012