# COMPACT SUMS OF TOEPLITZ PRODUCTS ON WEIGHTED DIRICHLET SPACE OF THE UNIT BALL

• Hu, Yinyin (Department of Mathematics Dalian Maritime university) ;
• Lu, Yufeng (School of Mathematical Sciences Dalian University of Technology)
• Accepted : 2019.03.04
• Published : 2019.03.31

#### 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.

#### Acknowledgement

Supported by : NSFC

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