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

## Keywords:

Self-adjoint, Norm-attainability, Norm, Elementary Operators## Abstract

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 *T _{A,B}: B(H)→B(H)* defined by

*T*and

_{A,B}(X) =AX B + BX A, ∀ X ∈ B(H)*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 T

_{A, B }is equal to the norm of T

_{A,B}when it is implemented by normal operators.

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## How to Cite

*MathLAB Journal*,

*5*, 12-22. Retrieved from http://purkh.com/index.php/mathlab/article/view/704

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Copyright (c) 2020 Benard Okelo

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