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Norms of elementary operators. (English) Zbl 1142.47023

Let \(A_k\) and \(B_k\), \(1\leq k\leq n\), be two sets of bounded linear operators on a Hilbert space \(H\). The authors prove that the norm of the elementary operator \(T: B(H)\to B(H)\) defined by \(T(X)= \sum^n_{k=1} A_k XB_k\), \(X\in B(H)\), is obtained on the unitary operators in \(B(H)\).

MSC:

47B47 Commutators, derivations, elementary operators, etc.
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
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References:

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