Norms of Inner Derivations on Norm ideals

Abstract

Let B(H) be the algebra of bounded linear operators on a Hilbert space H and J be a norm ideal in B(H). We investigate the relationship between the diameter of the numerical range of an operator A ∈ B(H) and the norm of inner derivation implemented by A on a norm ideal J. Further, we consider the applications of S - universality to the above relationship. Mathematics Subject Classification: Primary 47B47; Secondary 47A12, 47A30