Metric versions of posner's theorems

摘要

Let S and T be continuous linear operators on an ultraprime Banach algebra A. We show that if S, T, and ST are close to satisfy the derivation identity on A, then either S or T approaches to zero. If T is close to satisfy the derivation identity and [T(a), a] is near the centre of A for each a ∈ A, then either T approaches to zero or A is nearly commutative. Further, we give quantitative estimates of these phenomena.