Commutant of analytic Toeplitz operators on the Bergman space
type: Item
instance of: scholarly article
title: Commutant of analytic Toeplitz operators on the Bergman space
zbMATH Open document ID: 1222.47037
author: Jia Yi Jiang
author: Sheng Di Xu
publication date: 2011-03-02T00:00:00Z
review text: The authors study the commutant of Toeplitz operators with polynomial symbols acting on the standard weighted Bergman space on the unit disk. Let \(\rho_F(T_p)\) denote the Fredholm domain of \(T_p\), \(\sigma(T_p)\) denote the spectrum of \(T_p\), and let \(\mathcal{A}'(T_p)\) denote the commutant of \(T_p\). The main result of the paper states that, given a polynomial \(p(z)\), \(\mathcal{A}'(T_p) = \mathcal{A}'(T_{z^l})\), where \(l=\min\{|\mathrm{index}(T_p - \lambda)| : \lambda \in \rho_F(T_p) \cap \sigma(T_p) \}\).
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 14Q05
zbMATH DE Number: 5859362
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: polynomial symbol
zbMATH Keywords: weighted Bergman space
zbMATH Keywords: commutant
MaRDI profile type: Publication
full work available at URL: s10114-010-0116-y
OpenAlex ID: W2072507716
cites work: The Commutant of an Analytic Toeplitz Operator
cites work: Q4101018
cites work: Similarity of analytic Toeplitz operators on the Bergman spaces
cites work: Lifting Syzygies and Extending Algebraic Vector Bundles
DOI: 10.1007/S10114-010-0116-Y
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5859362