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Joint Continuity of Bi-multiplicative Functionals

Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 2)

Publication Date:

Authors : ; ;

Page : 33-44

Keywords : Jointly continuous; Bi-multiplicative functional; Almost bi-multiplicative;

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Abstract

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 $n=2$. 

Last modified: 2021-11-03 14:32:34