1. Consider a Banach space X and let B(X) be the algebra of linear- bounded operators on 3Z. If T, S, X E B(3E) we may define on B(X) the opera- tor C( T, S) X = TX - XS, which is often called the commutator of T and S. We denote px(T, S) = !E /I C(T, S)n X jjlln. This number can be considered as a “spectral distance” from S to T with regard to X, being intimately connected with spectral properties of T and S at least in the case when these have the single-valued extension property [l] (in particular if they are decomposable [2]). If X = I then (see [3]) C(T, S)” I = (T - S)[%l = f (- l)k (;) T”-kSk