\(m\)-isometries, \(n\)-symmetries and other linear transformations which are hereditary roots
type: Item
instance of: scholarly article
title: \(m\)-isometries, \(n\)-symmetries and other linear transformations which are hereditary roots
zbMATH Open document ID: 1284.47015
author: Mark Stankus
published in: Integral Equations and Operator Theory
publication date: 2013-04-15T00:00:00Z
review text: The author develops techniques to study bounded linear transformations \(T\) of a complex Hilbert space such that \(\sum_{m,n} c_{m,n} T^{*n} T^m=0\), where \(c_{m,n} \in C\) and all but finitely many \(c_{m,n}\) are zero. Such an operator is called a hereditary root of the polynomial \(p(x,y)=\sum_{m,n} c_{m,n} y^{n} x^m\). The techniques developed include finding maximal invariant subspaces satisfying certain operator-theoretic properties, a description of the spectral picture of a root, resolvent inequalities for a root, and additional properties which can be derived when knowing more about the spectrum of a particular root.
reviewed by: Mikhail Yu. Kokurin
Mathematics Subject Classification ID: 47A62
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 6153941
zbMATH Keywords: hereditary functional calculus
zbMATH Keywords: resolvent inequality
zbMATH Keywords: hereditary root
zbMATH Keywords: factoring
zbMATH Keywords: reducing subspace
zbMATH Keywords: isometry
MaRDI profile type: Publication
full work available at URL: s00020-012-2026-0
OpenAlex ID: W2471320343
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DOI: 10.1007/S00020-012-2026-0
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description: scientific article; zbMATH DE number 6153941