Khoddami, A. (2018). A Certain Class of Character Module Homomorphisms on Normed Algebras. Sahand Communications in Mathematical Analysis, 12(1), 113-120. 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, 12, 1, 2018, 113-120. 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, 12(1), pp. 113-120. 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; 12(1): 113-120. doi: 10.22130/scma.2018.78500.364

A Certain Class of Character Module Homomorphisms on Normed Algebras

^{}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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