Strongly zero product determined Banach algebras

C⁎-algebras, group algebras, and the algebra A(X) of approximable operators on a Banach space X having bounded approximation property are known to be zero product determined. In this paper we give quantitative estimate by showing that, for A, there exists constant α with that every continuous bilinear functional φ:A×A→C linear ξ A such thatsup‖a‖=‖b‖=1⁡|φ(a,b)−ξ(ab)|≤αsup‖a‖=‖b‖=1,ab=0⁡|φ(a,b)| in each following cases: (i) is C⁎-algebra, which case α=8; (ii) A=L1(G) locally compact G, α=60271+sin⁡π101−2sin⁡π10; (iii) A=A(X) (A) (which rather strong X), α=60271+sin⁡π101−2sin⁡π10C2, where C associated require X.