A Banach algebra A is said to be zero Lie product determined Banach algebra if for every continuous bilinear functional φ : A × A --> C the following holds: if φ(a; b) = 0 whenever ab = ba, then there exists some τ 2 A∗ such that φ(a; b) = τ(ab − ba) for all a; b 2 A. We show that any finite nest algebra over a complex Hilbert space is a zero Lie product determined Banach algebra
