On generalized numerical range of the Aluthge transformation.
type: Item
instance of: scholarly article
title: On generalized numerical range of the Aluthge transformation.
zbMATH Open document ID: 1033.15022
DOI: 10.1016/S0024-3795(03)00383-5
author: Masatoshi Ito
author: Hiroshi Nakazato
author: Kazuyoshi Okubo
author: Takeaki Yamazaki
published in: Linear Algebra and its Applications
publication date: 2003-08-25T00:00:00Z
review text: Let \(T\) be a bounded linear operator on a Hilbert space. The Aluthge transform \(\widetilde{T}\) of \(T\) is given by \(\widetilde{T} =| T| ^{1/2}U| T| ^{1/2}\) where \(T=U | T | \) is the polar decomposition of \(T\). The authors show that the Aluthge transformation \(\widetilde T\) of a matrix \(T\) and a polynomial \(f\) satisfy the inclusion \(W_C(f(\widetilde T))\subset W_C(f(T))\) for the generalized numerical range \(W_C(\cdot)\) if \(C\) is a Hermitian matrix or a rank-one matrix.
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 47A12
Mathematics Subject Classification ID: 47A63
zbMATH DE Number: 1970615
zbMATH Keywords: Aluthge transformation
zbMATH Keywords: generalized numerical range
zbMATH Keywords: majorization
zbMATH Keywords: Hilbert space
zbMATH Keywords: Hermitian matrix
reviewed by: A. R. Alimov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1970615