On the double commutant of Cowen-Douglas operators
type: Item
instance of: scholarly article
title: On the double commutant of Cowen-Douglas operators
zbMATH Open document ID: 1230.47036
author: Li Chen
author: Ronald G. Douglas
author: Kunyu Guo
published in: Journal of Functional Analysis
publication date: 2011-03-21T00:00:00Z
review text: It is shown as the main result of this paper that for any Cowen-Douglas operator \(T\in B_n(\Omega)\) [\textit{M. J. Cowen} and \textit{R.G. Douglas}, Acta Math. 141, 187--261 (1978; Zbl 0427.47016)], the von Neumann algebra \(V^*(T)\) consisting of operators commuting with \(T\) and \(T^*\) is isomorphic the commutant of matrix algebra \(M({\mathcal N}, \otimes {\mathcal M})\in M_n(C)\) which is generated by the curvature \({\mathcal K}\) and its covariant derivatives \({\mathcal K}_{z^i, \overline{z}^j}\), where \({\mathcal K}\) is the curvature of the bundle \((E_T, D)\) determined by \(T\). By this theorem, the authors give a geometrical characterization of \(V^*(T)\).
reviewed by: Kui Ji
Mathematics Subject Classification ID: 47A65
Mathematics Subject Classification ID: 47C15
zbMATH DE Number: 5868416
zbMATH Keywords: Cowen-Douglas operator
zbMATH Keywords: von Neumann algebra
zbMATH Keywords: reducing subspace
zbMATH Keywords: connection
MaRDI profile type: Publication
full work available at URL: j.jfa.2010.12.030
OpenAlex ID: W2005511086
cites work: A class of subnormal operators related to multiply-connected domains
cites work: Complex geometry and operator theory
cites work: Equivalence of connections
cites work: Multiplication operators on the Bergman space via analytic continuation
cites work: Density of algebras generated by Toeplitz operators on Bergman spaces
cites work: Q5391214
cites work: Multiplication operators defined by covering maps on the Bergman space: the connection between operator theory and von Neumann algebras
cites work: Multiplication operators on the Bergman space via the Hardy space of the bidisk
cites work: Reducing subspace of analytic Toeplitz operators on the Bergman space
cites work: Q3995501
cites work: Similarity classification of holomorphic curves
cites work: Q5677789
cites work: Reducing Subspaces for a Class of Multiplication Operators
DOI: 10.1016/J.JFA.2010.12.030
Recommended article: Q3590821
Recommended article: Q5318488
Recommended article: Double commutants of multiplication operators on $C(K).$
Recommended article: Q4265764
Recommended article: On the double commutant expectation property for operator systems
Recommended article: Q5482093
Recommended article: Approximate double commutants in von Neumann algebras and C*-algebras
Recommended article: The double commutant property for composition operators
Recommended article: A note on doubly commuting tuples of hyponormal operators on Hilbert spaces
Recommended article: Q4718125
description: scientific article; zbMATH DE number 5868416