The norm of a symmetric elementary operator

Magajna, Bojan

doi:10.1090/S0002-9939-03-07248-4

The norm of a symmetric elementary operator
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Proc. Amer. Math. Soc. 132 (2004), 1747-1754 Request permission

Abstract:

The norm of the operator $x\mapsto a^*xb+b^*xa$ on $A= {\mathrm B}(\mathcal {H})$ (or on any prime C$^*$-algebra $A$) is computed for all $a,b\in A$ and is shown to be equal to the completely bounded norm.

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