@article { author = {Zivari-Kazempour, Abbas and Valaei, Mohamad}, title = {Joint Continuity of Bi-multiplicative Functionals}, journal = {Sahand Communications in Mathematical Analysis}, volume = {18}, number = {2}, pages = {33-44}, year = {2021}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2020.127223.795}, 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 $n=2$. }, keywords = {Jointly continuous,Bi-multiplicative functional,Almost bi-multiplicative}, url = {https://scma.maragheh.ac.ir/article_240861.html}, eprint = {https://scma.maragheh.ac.ir/article_240861_4cf7ace48b030867b9ea59fa675983ee.pdf} }