Khoddami, A. (2018). A certain class of character module homomorphisms on normed algebras. Sahand Communications in Mathematical Analysis, (), -. doi: 10.22130/scma.2018.78500.364

Ali Reza Khoddami. "A certain class of character module homomorphisms on normed algebras". Sahand Communications in Mathematical Analysis, , , 2018, -. doi: 10.22130/scma.2018.78500.364

Khoddami, A. (2018). 'A certain class of character module homomorphisms on normed algebras', Sahand Communications in Mathematical Analysis, (), pp. -. doi: 10.22130/scma.2018.78500.364

Khoddami, A. A certain class of character module homomorphisms on normed algebras. Sahand Communications in Mathematical Analysis, 2018; (): -. doi: 10.22130/scma.2018.78500.364

A certain class of character module homomorphisms on normed algebras

Articles in Press, Accepted Manuscript , Available Online from 28 May 2018

^{}Faculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box 3619995161-316, Shahrood, Iran.

Abstract

For two normed algebras $A$ and $B$ with the character space $\bigtriangleup(B)\neq \emptyset$ and a left $B-$module $X,$ a certain class of bounded linear maps from $A$ into $X$ is introduced. We set $CMH_B(A, X)$ as the set of all non-zero $B-$character module homomorphisms from $A$ into $X$. In the case where $\bigtriangleup(B)=\lbrace \varphi\rbrace$ then $CMH_B(A, X)\bigcup \lbrace 0\rbrace$ is a closed subspace of $L(A, X)$ of all bounded linear operators from $A$ into $X$. We define an equivalence relation on $CMH_B(A, X)$ and use it to show that $CMH_B(A, X)\bigcup\lbrace 0\rbrace $ is a union of closed subspaces of $L(A, X)$. Also some basic results and some hereditary properties are presented. Finally some relations between $\varphi-$amenable Banach algebras and character module homomorphisms are examined.

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