Semigroups of operators on quotient spaces of \(H^ 2\)
type: Item
instance of: scholarly article
title: Semigroups of operators on quotient spaces of \(H^ 2\)
zbMATH Open document ID: 0770.47016
DOI: 10.1016/0022-247X(92)90252-9
author: Steven M. Seubert
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-01-16T00:00:00Z
review text: Let \(\phi\) be an inner function on the unit disc \(\mathbb{D}=\{z\in\mathbb{C}: | z| <1\}\); \(S\) be standard unilateral shift on \(H^ 2(\mathbb{D})\), i.e. \(S: f(z)\to zf(z)\); \(S_ \phi\) is the compression of \(S\) onto \(H^ 2/\phi H^ 2\); \(A(\phi)\) is the commutant of \(S_ \phi\). A sufficient condition for a fixed operator in \(A(\phi)\) to be embeddable in a \(C_ 0\)-semigroup of operators in \(A(\phi)\) is given. If this semigroup consists of contraction operators, then this condition is necessary.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 91587
zbMATH Keywords: inner function on the unit disc
zbMATH Keywords: unilateral shift
zbMATH Keywords: compression
zbMATH Keywords: commutant
reviewed by: Michael Perelmuter
MaRDI profile type: Publication
cites work: Q5549343
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description: scientific article; zbMATH DE number 91587