On zero product determined Banach algebras

Let A be a Banach algebra with a left approximate identity. In this paper, under each of the following conditions, we prove that A is zero product determined. (i) For every continuous bilinear mapping from A A into X, where X is a Banach space, there exists k > 0 such that k(a; b)k kkabk, for all a; b 2 A. (ii) A is generated by idempotents.