Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2019; 34(2): 533-542

Online first article June 29, 2018      Printed April 30, 2019

https://doi.org/10.4134/CKMS.c180148

Copyright © The Korean Mathematical Society.

Commutants of Toeplitz operators with polynomial symbols on the Dirichlet space

Yong Chen, Young Joo Lee

Hangzhou Normal University; Chonnam National University

Abstract

We study commutants of Toeplitz operators acting on the Dirichlet space of the unit disk and prove that an operator in the Toeplitz algebra commuting with a Toeplitz operator with a nonconstant polynomial symbol must be a Toeplitz operator with an analytic symbol.

Keywords: commutant, Toeplitz operator, Dirichlet space

MSC numbers: Primary 47B35; Secondary 32A37