A remark on the essential spectra of Toeplitz operators with bounded measurable coefficients
type: Item
instance of: scholarly article
title: A remark on the essential spectra of Toeplitz operators with bounded measurable coefficients
zbMATH Open document ID: 1122.47026
author: Eugene Shargorodsky
published in: Integral Equations and Operator Theory
publication date: 2007-05-03T00:00:00Z
review text: Let \(\mathbb T\) be the unit circle and consider the Hardy space \(H^p(\mathbb T):=P L^p(\mathbb T)\), where \(P\) is the Riesz projection and \(1<p<\infty\). The paper presents a sufficient condition for a point to belong to the essential spectrum of a Toeplitz operator \(T(a) : H^p(\mathbb T) \to H^p(\mathbb T)\), \(T(a)f = P(af)\), generated by a function \(a\in L^\infty(\mathbb T)\). The condition is based on geometric properties of the cluster values of \(a\).
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 45E05
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 5149194
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: essential spectra
zbMATH Keywords: Fredholm operator
zbMATH Keywords: cluster values
reviewed by: L. P. Castro
MaRDI profile type: Publication
full work available at URL: s00020-006-1470-0
OpenAlex ID: W1970918658
DOI: 10.1007/S00020-006-1470-0
description: scientific article; zbMATH DE number 5149194