Bulletin of the
Korean Mathematical Society
BKMS

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

Article

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Bull. Korean Math. Soc. 2019; 56(2): 319-331

Online first article March 13, 2019      Printed March 1, 2019

https://doi.org/10.4134/BKMS.b180020

Copyright © The Korean Mathematical Society.

Compact sums of Toeplitz products on weighted Dirichlet space of the unit ball

Yinyin Hu, Yufeng Lu

Dalian Maritime university; Dalian University of Technology

Abstract

On the weighted Dirichlet space, by the Sobolev's embedding theorem, we characterize the compactness for operators which are finite sums of products of several Toeplitz operators. Moreover, the essential spectrum of Toeplitz operator is characterized.

Keywords: Toeplitz operator, compactness, weighted Dirichlet space

MSC numbers: Primary 47B35

Supported by: This work was financially supported by NSFC No. 11671065