A dichotomy for linear spaces of Toeplitz operators
type: Item
instance of: scholarly article
title: A dichotomy for linear spaces of Toeplitz operators
zbMATH Open document ID: 0922.47021
author: Marek Ptak
author: Edward A. Azoff
published in: Journal of Functional Analysis
publication date: 1999-10-17T00:00:00Z
review text: For a Hilbert space \(H\), \(B(H)\) denotes the algebra of all bounded linear operators on \(H\); and the reflexive closure of a subspace \(S\) in \(B(H)\) is defined by: \[ \text{ref}(S)= \{T\in B(H); T(f)\in\overline{S(f)}, \forall f\in H\}. \] \(S\) is said to be reflexive if \(\text{ref}(S)= S\), and transitive if \(\text{ref}(S)= B(H)\). In this paper, the authors proved that: Every intransitive and ultraweakly closed subspace of the space \(F\) of all Toeplitz operators is reflexive. Every proper and ultraweakly closed subspace of \(F\) which contains the algebra of analytic Toeplitz operators is reflexive. This result extends a theorem of D. Sarason: the algebra of analytic Toeplitz operators is reflexive.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 47A15
zbMATH DE Number: 1214160
zbMATH Keywords: ultraweakly closed subspace
MaRDI profile type: Publication
OpenAlex ID: W2094602282
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DOI: 10.1006/JFAN.1998.3275
description: scientific article; zbMATH DE number 1214160