Complex symmetric weighted composition operators on H2(D)

Sungeun Jung; Yoenha Kim; Eungil Ko; Ji Eun Lee

doi:10.1016/j.jfa.2014.04.004

Complex symmetric weighted composition operators on H²(D)

Sungeun Jung, Yoenha Kim, Eungil Ko, Ji Eun Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

72 Scopus citations

Abstract

In this paper we study complex symmetric weighted composition operators on the Hardy space. We provide some characterizations of ψ and φ when a weighted composition operator W_ψ,φ is complex symmetric. We investigate which combinations of weights ψ and maps of the open unit disk φ give rise to complex symmetric weighted composition operators with a special conjugation. As some applications, we obtain several examples for nonnormal complex symmetric operators. In addition, we give spectral properties of complex symmetric weighted composition operators. We examine eigenvalues and eigenvectors of such operators and find some conditions for which a complex symmetric weighted composition operator is Hilbert-Schmidt. Finally, we consider cyclicity, hypercyclicity, and the single-valued extension property for complex symmetric weighted composition operators.

Original language	English
Pages (from-to)	323-351
Number of pages	29
Journal	Journal of Functional Analysis
Volume	267
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2014.04.004
State	Published - 15 Jul 2014

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIP) (No. 2009-0083521 ).

Keywords

Complex symmetric
Hilbert-Schmidt
The single-valued extension property
Weighted composition operator

Access to Document

10.1016/j.jfa.2014.04.004

Cite this

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abstract = "In this paper we study complex symmetric weighted composition operators on the Hardy space. We provide some characterizations of ψ and φ when a weighted composition operator Wψ,φ is complex symmetric. We investigate which combinations of weights ψ and maps of the open unit disk φ give rise to complex symmetric weighted composition operators with a special conjugation. As some applications, we obtain several examples for nonnormal complex symmetric operators. In addition, we give spectral properties of complex symmetric weighted composition operators. We examine eigenvalues and eigenvectors of such operators and find some conditions for which a complex symmetric weighted composition operator is Hilbert-Schmidt. Finally, we consider cyclicity, hypercyclicity, and the single-valued extension property for complex symmetric weighted composition operators.",

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AB - In this paper we study complex symmetric weighted composition operators on the Hardy space. We provide some characterizations of ψ and φ when a weighted composition operator Wψ,φ is complex symmetric. We investigate which combinations of weights ψ and maps of the open unit disk φ give rise to complex symmetric weighted composition operators with a special conjugation. As some applications, we obtain several examples for nonnormal complex symmetric operators. In addition, we give spectral properties of complex symmetric weighted composition operators. We examine eigenvalues and eigenvectors of such operators and find some conditions for which a complex symmetric weighted composition operator is Hilbert-Schmidt. Finally, we consider cyclicity, hypercyclicity, and the single-valued extension property for complex symmetric weighted composition operators.

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