Document Type : Research Paper

Author

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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