Norms of Derivations Implemented by S-Universal Operators

Abstract

Let H be a complex Hilbert space and B(H) the algebra of all bounded linear operators on H. For A, B ∈ B(H), we define inner derivations implemented by A,B respectively on B(H) by ΔA(X) = AX−XA, ΔB(X) = BX−XB and a generalized derivation by ΔA,B(X) = AX − XB, ∀X ∈ B(H). We establish the relationship between the norms of ΔA, ΔB and ΔA,B on B(H), specifically, when the operators A, B are S - universal. Mathematics Subject Classification: Primary 47B47; Secondary 47A12, 47A30