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On essential norm of elementary operator \(\Gamma: T\to ATB\). (Chinese. English summary) Zbl 0696.47008

Summary: This paper describes the relation between essential norm of the operator \(\Gamma: T\to ATB\) and those of operators A and B. It is shown that \[ \| \Gamma \|_ e=\max \{\| A\|_ e\| B\|,\| A\| \| B\|_ e\}. \]

MSC:

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