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Essential maximal numerical range of the Aluthge transform. (Chinese. English summary) Zbl 1363.47012

Summary: Let \(H\) be a Hilbert space and for any bounded linear operator \(T\) in \(H\), denote by \(\tilde{T}^t\), \(\tilde{T}^{t(*)}\) the generalized Aluthge transform and the generalized \(*\)-Aluthge transform of \(T\), respectively, where \(t\in(0,1)\). By the method of operational partitioning, the relationship of the essential norm between \(\tilde{T}^t\) and \(\tilde{T}^{t(*)}\) is given. Also, the essential maximal numerical ranges of \(\tilde{T}^t\) and \(\tilde{T}^{t(*)}\) are discussed for \(t=1/2\).

MSC:

47A12 Numerical range, numerical radius
47A10 Spectrum, resolvent
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