On weakly unitarily invariant norm and the Aluthge transformation
type: Item
instance of: scholarly article
title: On weakly unitarily invariant norm and the Aluthge transformation
zbMATH Open document ID: 1029.15025
DOI: 10.1016/S0024-3795(03)00485-3
author: D. Massart
published in: Linear Algebra and its Applications
publication date: 2003-09-09T00:00:00Z
review text: The main result: \(|||f(P^\lambda UP^{1-\lambda})|||\leq \max\{|||f(T)|||, |||U^* f(T)U+ f(0)(I- U^* U)|||\}\), where \(T\in B(H)\) is a bounded linear operator on a Hilbert space \(H\), \(f\) is a polynomial, and \(|||\cdot|||\) is a seminorm on \(H\) which satisfies the following two conditions: a) \(\exists\gamma> 0\) such that \(|||X|||\leq \gamma\|X\|\) \(\forall X\in B(H)\), and b) \(\|||S^*XS|||\leq \|S\|^2|||X|||\) \(\forall X\), \(S\in B(H)\); here \(\|\cdot\|\) is the Hilbert operator norm. As a consequence of this fact it is proved that for some seminorms (including the \(\rho\)-radii, \(0< \rho\leq 2\)), \(|||f(P^\lambda UP^{1-\lambda})|||\leq |||f(T)|||\).
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 47A12
Mathematics Subject Classification ID: 47A63
zbMATH DE Number: 1978125
zbMATH Keywords: weakly unitarily invariant norm
zbMATH Keywords: Aluthge transformation
zbMATH Keywords: matrix norm
zbMATH Keywords: Hilbert space
reviewed by: A. R. Alimov
MaRDI profile type: Publication
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full work available at URL: s0024-3795(03)00485-3
OpenAlex ID: W2084341246
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description: scientific article; zbMATH DE number 1978125