Joint Continuity of Bi-multiplicative Functionals
Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 2)Publication Date: 2021-05-01
Authors : Abbas Zivari-Kazempour; Mohamad Valaei;
Page : 33-44
Keywords : Jointly continuous; Bi-multiplicative functional; Almost bi-multiplicative;
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 $n=2$.
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Last modified: 2021-11-03 14:32:34