Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19368120210701A note on zero Lie product determined nest algebras as Banach algebrasA note on zero Lie product determined nest algebras as Banach algebras1624522210.22072/wala.2020.130358.1293ENHogerGhahramaniDepartment of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, Iran.KamalFallahiDepartment of Mathematics, Payam Noor University of Technology, P.O. Box 19395-3697, Tehran, Iran.0000-0003-3400-4424WaniaKhodakaramiDepartment of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, Iran.Journal Article20200704A Banach algebra $\A$ is said to be zero Lie product determined Banach algebra if for every continuous bilinear functional $\phi:\A \times \A\rightarrow \mathbb{C}$ the following holds: if $\phi(a,b)=0$ whenever $ab=ba$, then there exists some $\tau \in \A^*$ such that $\phi(a,b)=\tau(ab-ba)$ for all $a,b\in \A$. We show that any finite nest algebra over a complex Hilbert space is a zero Lie product determined Banach algebra.http://wala.vru.ac.ir/article_245222_bba88ea53ec7d84e8f04748e3bd83bb6.pdf