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Characterizations of Hankel operators in the essential commutant of quasicontinuous Toeplitz operators

Part of: Function theory on the disc Commutative Banach algebras and commutative topological algebras Special classes of linear operators

Published online by Cambridge University Press:  09 February 2021

Yi Yan
Yi Yan*
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, KS66045, USA
*
e-mail: yiyan@ku.edu
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Abstract

This note characterizes, in terms of interpolating Blaschke products, the symbols of Hankel operators essentially commuting with all quasicontinuous Toeplitz operators on the Hardy space of the unit circle. It also shows that such symbols do not contain the complex conjugate of any nonconstant singular inner function.

Keywords

Hankel operatorToeplitz operatorquasicontinuousDouglas algebrainterpolating Blaschke productsingular inner function

MSC classification

Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Secondary: 46J10: Banach algebras of continuous functions, function algebras 30J05: Inner functions
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 1 , March 2022 , pp. 44 - 51
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Copyright
© Canadian Mathematical Society 2021

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