MathLAB Journal

Norms of Self-Adjoint Two-Sided Multiplication Operators in Norm-Attainable Classes

Abstract

Benard Okelo

Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H. In this note, we give
characterizations when the elementary operator TA;B : B(H) ! B(H) defined by TA;B(X) = AXB + BXA; 8 X 2
B(H) and A; B fixed in B(H) is self adjoint and implemented by norm-attainable operators. We extend our work by
showing that the norm of the adjoint of TA;B is equal to the norm of TA;B when it is implemented by normal operators.