The norm of a symmetric elementary operator
Bojan Magajna · Proceedings of the American Mathematical Society · 2003
The norm of the operator x ↦ a ∗ x b + b ∗ x a x\mapsto a^*xb+b^*xa on A = B ( H ) A= {\mathrm B}(\mathcal {H}) (or on any prime C ∗ ^* -algebra A A ) is computed for all a , b ∈ A a,b\in A and is shown to be equal to the completely bounded norm.