Unbounded dissipative compressed Toeplitz operators.
type: Item
instance of: scholarly article
title: Unbounded dissipative compressed Toeplitz operators.
zbMATH Open document ID: 1059.47031
author: Steven M. Seubert
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-03-14T00:00:00Z
review text: Let \({\mathcal C}\) be the collection of all closed densely defined linear maps commuting with the adjoint of the compression of the standard unilateral shift on the Hardy space of the unit disc to a shift coinvariant subspace. A linear map \(T\) with the domain \(D(T)\) dense in a Hilbert space is said to be dissipative on \(D(T)\) if \(\langle Tx,x\rangle\) has nonnegative imaginary part for all \(x\in D(T)\). In the paper under review, the author proves necessary and sufficient conditions for a linear map in \({\mathcal C}\) to be dissipative using a characterization of linear maps comprising \({\mathcal C}\), due to \textit{D. Suárez} [Pac. J. Math. 179, 371--396 (1997; Zbl 0895.47021)] and a characterization of dissipative operators as the infinitesimal generators of \(C_0\)-semigroups of contraction operators, due to \textit{R. S. Phillips} [Trans. Am. Math. Soc. 90, 193-254 (1959; Zbl 0093.10001)].
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47B44
Mathematics Subject Classification ID: 47A20
zbMATH DE Number: 2055369
zbMATH Keywords: unbounded Toeplitz operator
zbMATH Keywords: dissipative operator
zbMATH Keywords: infinitesimal generator of \(C_0\)-semigroup
reviewed by: Oleksiy Karlovych
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.09.016
OpenAlex ID: W2081376348
cites work: Q3244654
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DOI: 10.1016/J.JMAA.2003.09.016
description: scientific article; zbMATH DE number 2055369