Norms of Self-Adjoint Two-Sided Multiplication Operators in Norm-Attainable Classes
Keywords:Self-adjoint, Norm-attainability, Norm, Elementary Operators
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) =AX B + BX A, ∀ X ∈ 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.
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