On some properties of Cowen-Douglas class of operators
type: Item
instance of: scholarly article
title: On some properties of Cowen-Douglas class of operators
zbMATH Open document ID: 1482.47060
DOI: 10.1155/2018/6078594
author: Parastoo Heiatian Naeini
author: Bahmann Yousefi
published in: Journal of Function Spaces
publication date: 2018-04-06T00:00:00Z
review text: Summary: We will consider multiplication operators on a Hilbert space of analytic functions on a domain \(\Omega \subset \mathbb{C}\). For a bounded analytic function \(\varphi\) on \(\Omega\), we will give necessary and sufficient conditions under which the complement of the essential spectrum of \(M_\varphi\) in \(\varphi (\Omega)\) becomes nonempty and this gives conditions for the adjoint of the multiplication operator \(M_\varphi\) belongs to the Cowen-Douglas class of operators. Also, we characterize the structure of the essential spectrum of a multiplication operator and we determine the commutants of certain multiplication operators. Finally, we investigate the reflexivity of a Cowen-Douglas class operator.
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 47B13
zbMATH DE Number: 6856696
zbMATH Keywords: multiplication operators
zbMATH Keywords: Hilbert space of analytic functions
zbMATH Keywords: essential spectrum
zbMATH Keywords: Cowen-Douglas class
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/6078594
OpenAlex ID: W2793119678
cites work: Complex geometry and operator theory
cites work: Generalized Bergman Kernels and the Cowen-Douglas Theory
cites work: Invariant Subspaces in Banach Spaces of Analytic Functions
cites work: On the Reflexivity of Operators on Function Spaces
cites work: On the multiplication operators on spaces of analytic functions
cites work: Operators in Cowen-Douglas classes
cites work: Q5708177
cites work: Q5607489
cites work: Reflexivity of the shift operator on some BK spaces
cites work: On intertwining operators via reproducing kernels
cites work: On the double commutant of Cowen-Douglas operators
cites work: Reducing subspaces of multiplication operators on function spaces
cites work: Flag structure for operators in the Cowen-Douglas class
cites work: A classification of homogeneous operators in the Cowen-Douglas class
cites work: Reflexivity of powers of the multiplication operators on special function spaces
cites work: Q4000087
description: scientific article; zbMATH DE number 6856696