## The norm of a derivation.(English)Zbl 0197.10501

Summary: In this paper, we determine the norm of the inner derivation $$\mathfrak Q_T\colon A \to TA - AT$$ acting on the Banach algebra $$\mathfrak B(H)$$ of all bounded linear operators on Hilbert space. More precisely, we show that $$\Vert\mathfrak Q_T\Vert = \inf\{2\,\Vert T - \lambad I\Vert : \lambda\] complex \(\}$$. If $$T$$ is normal, then $$\Vert\mathfrak Q_T\Vert can be specified in terms of the geometry of the spectrum of \(T$$.

### MSC:

 47-XX Operator theory 46-XX Functional analysis
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