TY - JOUR
ID - 375
TI - Banach module valued separating maps and automatic continuity
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Mousavi, L.
AU - Sady, F.
AD -
Y1 - 2011
PY - 2011
VL - 37
IS - No. 4
SP - 127
EP - 139
KW - Banach algebras
KW - Banach modules
KW - separating maps
KW - cozero set
KW - point multiplier
KW - Automatic continuity
DO -
N2 - For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear separating map $T:B longrightarrow X$, where $B$ is a unital commutative semisimple regular Banach algebra satisfying the Ditkin's condition and $X$ is a left Banach module over a unital commutative Banach algebra. We also show that if $X$ is hyper semisimple and $T$ is bijective, then $T$ is automatically continuous and $T^{-1}$ is separating as well.
UR - http://bims.iranjournals.ir/article_375.html
L1 - http://bims.iranjournals.ir/article_375_1bbfb6fc763d4e986298a5e63f05fd4c.pdf
ER -