TY - JOUR
ID - 240861
TI - Joint Continuity of Bi-multiplicative Functionals
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Zivari-Kazempour, Abbas
AU - Valaei, Mohamad
AD - Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.
Y1 - 2021
PY - 2021
VL - 18
IS - 2
SP - 33
EP - 44
KW - Jointly continuous
KW - Bi-multiplicative functional
KW - Almost bi-multiplicative
DO - 10.22130/scma.2020.127223.795
N2 - For Banach algebras $mathcal{A}$ and $mathcal{B}$, we show that if $mathfrak{A}=mathcal{A}times mathcal{B}$ is unital, then each bi-multiplicative mapping from $mathfrak{A}$ into a semisimple commutative Banach algebra $mathcal{D}$ is jointly continuous. This conclusion generalizes a famous result due to$check{text{S}}$ilov, concerning the automatic continuity of homomorphisms between Banach algebras. We also prove that every $n$-bi-multiplicative functionals on $mathfrak{A}$ is continuous if and only if it is continuous for the case $n=2$.
UR - https://scma.maragheh.ac.ir/article_240861.html
L1 - https://scma.maragheh.ac.ir/article_240861_e6375ff83f49e906b56ffeaaf06256ae.pdf
ER -