Normal boundary dilations and rationally invariant subspaces
type: Item
instance of: scholarly article
title: Normal boundary dilations and rationally invariant subspaces
zbMATH Open document ID: 0784.47007
DOI: 10.1007/BF01200695
author: H. Bercovici
author: W. S. Li
published in: Integral Equations and Operator Theory
publication date: 1993-06-29T00:00:00Z
review text: For a given Hilbert space operator \(T\) acting on some complex space \(H\), the authors use the following concept of spectral set. A nonvoid, compact subset \(K\) of the complex plane is said to be a spectral set for \(T\) if the norm of \(f(T)\) is less than the supremum of \(| f(\lambda)|\) as \(\lambda\) runs in \(K\), for each \(f\), a rational function with poles off \(K\). The main result is as follows. If \(G\) is a bounded domain in the complex plane, such that its boundary consists of a finite number of Jordan curves, its closure is a spectral set for \(T\), and the boundary of its closure is contained by the spectrum of \(T\), then there is a closed, nontrivial subspace of \(H\) invariated by \(f(T)\) for each rational function \(f\) with poles off the closure of \(G\).
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 47A45
zbMATH DE Number: 222144
zbMATH Keywords: rationally invariant subspace
zbMATH Keywords: Hilbert space operator
zbMATH Keywords: spectral set
reviewed by: V. Matache
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 222144