Abstract

Let T be bounded linear operator on a complex separable Hilbert space \(\mathcal H\). Let \(\widetilde{T}\) and \(\widetilde{T}^{*}\) be the Aluthge transform and *-Aluthge transform of T respectively. In this article, we discuss that the relations between the reduced minimal numerical range and modulus of \(\widetilde{T}-\lambda I\) and \(\widetilde{T}^{(*)}-\lambda I,\) respectively.KeywordsNumerical rangealuthge transformminimal numerical rangepolar decomposition

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