A commutator approach to truncated singular integral operators
type: Item
instance of: scholarly article
title: A commutator approach to truncated singular integral operators
zbMATH Open document ID: 1395.45007
author: Caixing Gu
author: Dong-O Kang
published in: Integral Equations and Operator Theory
publication date: 2018-06-08T00:00:00Z
review text: The authors develop an approach from the paper by \textit{C. Gu} [Taiwanese J. Math. 20, No. 1, 161--189 (2016; Zbl 1357.45010)] for the study of the normality of a class of the so-called truncated singular integral operators. More specifically, they focus on self-adjoint, isometric, coisometric and normal truncated singular integral operators with Cauchy kernel on the unit circle. The operators of such a type were introduced in the paper by \textit{E. Ko} and \textit{J. E. Lee} [Complex Anal. Oper. Theory 10, No. 4, 815--833 (2016; Zbl 1369.47034)] and they possess certain connections with dilations of operators and truncated Toeplitz operators. In the case of bounded coefficients involved in the construction of such operators, the authors give conditions on such coefficients under which the operator is self-adjoint or normal. They also give a condition for the equivalence of isometry, coisometry and unitarity property for such operators.
reviewed by: Alexey N. Karapetyants
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 6882303
zbMATH Keywords: singular integral operator
zbMATH Keywords: Cauchy kernel
zbMATH Keywords: Toeplitz operators
MaRDI profile type: Publication
full work available at URL: s00020-018-2429-7
OpenAlex ID: W2791772419
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DOI: 10.1007/S00020-018-2429-7
description: scientific article; zbMATH DE number 6882303