%0 Journal Article
%T Joint Continuity of Bi-multiplicative Functionals
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Zivari-Kazempour, Abbas
%A Valaei, Mohamad
%D 2020
%\ 12/27/2020
%V
%N
%P -
%! Joint Continuity of Bi-multiplicative Functionals
%K Jointly continuous
%K Bi-multiplicative functional
%K Almost bi-multiplicative
%R 10.22130/scma.2020.127223.795
%X 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 $n=2$.
%U