A commutator approach to truncated singular integral operators
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.
scientific article; zbMATH DE number 6882303
scientific article