Liu, Ni; Li, Bingjie Essential maximal numerical range of the Aluthge transform. (Chinese. English summary) Zbl 1363.47012 J. Anhui Univ., Nat. Sci. 40, No. 2, 9-13 (2016). 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 Keywords:generalized Aluthge transform; polar decomposition; essential spectrum; essential maximal numerical range PDFBibTeX XMLCite \textit{N. Liu} and \textit{B. Li}, J. Anhui Univ., Nat. Sci. 40, No. 2, 9--13 (2016; Zbl 1363.47012) Full Text: DOI