Complex symmetric Toeplitz operators on the Dirichlet space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Li, Anshui¹  Liu, Ya²  Chen, Yong¹ 

[1] Hangzhou Normal Univ, Dept Math, Hangzhou 311121, Peoples R China

[2] Zhejiang Normal Univ, Coll Chem & Life Sci, Jinhua 321004, Zhejiang, Peoples R China

关键词: Toeplitz operator;    Dirichlet space;    Complex symmetric operator;   

DOI  :  10.1016/j.jmaa.2020.123998

来源: Elsevier

【 摘 要 】

We study when a Toeplitz operator To on the Dirichlet space of the unit disk is complex symmetric with respect to a class of conjugations and find surprisingly that the case of complex symmetries of Toeplitz operators according to these conjugations is very few. We also show that if T-phi is complex symmetric, then the curve phi vertical bar(T) (T) must be nowhere winding. Furthermore, the spectrum and invertibility of complex symmetric Toeplitz operators are described. (C) 2020 Published by Elsevier Inc.

【 授权许可】

Free