TY - JOUR ID - 251152 TI - On zero product determined Banach algebras JO - Wavelet and Linear Algebra JA - WALA LA - en SN - 2383-1936 AU - Zivari-Kazempour, Abbas AD - Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran Y1 - 2022 PY - 2022 VL - 8 IS - 2 SP - 63 EP - 69 KW - Banach algebra KW - Zero product determined KW - idempotent KW - Approximate identity DO - 10.22072/wala.2021.540223.1348 N2 - Let $\mathcal{A}$ be a Banach algebra with a left approximate identity.    In this paper, under each of the following conditions, we prove that $\mathcal{A}$ is zero product determined.        (i) For every continuous bilinear mapping $\phi$ from ${\mathcal A}\times {\mathcal A}$ into ${\mathcal X}$, where ${\mathcal X}$ is a Banach space, there exists $k>0$ such that     $\Vert \phi(a,b)\Vert\leq k \Vert ab\Vert$, for all $a,b\in\mathcal{A}$.        (ii) $\mathcal{A}$ is generated by idempotents. UR - https://wala.vru.ac.ir/article_251152.html L1 - https://wala.vru.ac.ir/article_251152_e784d1a940100a0b25d41a003aab6bb4.pdf ER -