Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2020; 57(2): 509-520

Online first article December 4, 2019      Printed March 31, 2020

https://doi.org/10.4134/BKMS.b190371

Copyright © The Korean Mathematical Society.

Fredholm Toeplitz operators on the Dirichlet spaces of the polydisk

Kyunguk Na

Hanshin University

Abstract

We study the Toeplitz operators on the holomorphic and pluriharmonic Dirichlet spaces of the polydisk in terms of when Toeplitz operator is Fredholm operator there. Consequently, we describe the essential spectrum of Toeplitz operators.

Keywords: Toeplitz operator, Dirichlet space, pluriharmonic Dirichlet space, Fredholm operator

MSC numbers: Primary 47B35; Secondary 32A37

Supported by: The author was supported by Hanshin University Research Grant.