TY - JOUR
ID - 31199
TI - A Certain Class of Character Module Homomorphisms on Normed Algebras
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Khoddami, Ali Reza
AD - Faculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box 3619995161-316, Shahrood, Iran.
Y1 - 2018
PY - 2018
VL - 12
IS - 1
SP - 113
EP - 120
KW - Character space
KW - Character module homomorphism
KW - Arens products
KW - $varphi-$amenability
KW - $varphi-$contractibility
DO - 10.22130/scma.2018.78500.364
N2 - 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 $bigtriangleup(B)=lbrace varphirbrace$ then $CMH_B(A, X)bigcup lbrace 0rbrace$ 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)bigcuplbrace 0rbrace $ 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.
UR - https://scma.maragheh.ac.ir/article_31199.html
L1 - https://scma.maragheh.ac.ir/article_31199_6d259fdf33f0dff36ef61b8685f930c1.pdf
ER -