A generalization of amenability for topological semigroups and semigroup algebras

Authors : M LASHKAREZADEH BAMİ, H SADEGHİ

Pages : 567-577

View : 26 | Download : 8

Publication Date : 2017-08-01

Article Type : Research Paper

Abstract :In this paper for two topological semigroups $S$ and $T$, and a continuous homomorphism $\varphi$ from $S$ into $T$, we introduce and study the concept of $insert ignore into journalissuearticles values(\varphi, T);$-derivations on $S$ and $\varphi$-amenability of $T$ and investigate the relations between these two concepts. For two Banach algebras $A$ and $B$ and a continuous homomorphism $\varphi$ from $A$ into $B$ we also introduce the notion of $insert ignore into journalissuearticles values(\varphi, B);$-amenability of $A$ and show that a foundation semigroup $T$ with identity is $\varphi$-amenable whenever the Banach algebra $M_ainsert ignore into journalissuearticles values(S);$ is $insert ignore into journalissuearticles values(\tilde{\varphi},M_ainsert ignore into journalissuearticles values(T););$-amenable, where $\tilde{\varphi}:Minsert ignore into journalissuearticles values(S);\to Minsert ignore into journalissuearticles values(T);$ denotes the unique extension of $\varphi$. An example is given to show that the converse is not true.
Keywords : Continuous homomorphism, semigroup, Banach algebra, varphi, T, derivation, varphi amenable