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_4cf7ace48b030867b9ea59fa675983ee.pdf ER -