Characterizations of Square Roots of Unitary Weighted Composition Operators on H2

Yoenha Kim; Eungil Ko

doi:10.1007/s11785-021-01193-5

Characterizations of Square Roots of Unitary Weighted Composition Operators on H²

Yoenha Kim, Eungil Ko

Department of Mathematics

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

3 Scopus citations

Abstract

In this paper we study the square roots of unitary weighted composition operators on the Hardy space H², i.e., W_f_,_φ when Wg,ψ=Wf,φ2 is unitary. In particular, we provide the explicit forms of the symbol functions φ and f of such W_f_,_φ. Moreover, we show that the square roots W_f_,_φ of a unitary weighted composition operator are normal. Finally, we investigate several properties of such W_f_,_φ.

Original language	English
Article number	14
Journal	Complex Analysis and Operator Theory
Volume	16
Issue number	1
DOIs	https://doi.org/10.1007/s11785-021-01193-5
State	Published - Jan 2022

Bibliographical note

Funding Information:
This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2019R1A6A1A11051177) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1F1A1058633). The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2020R1I1A1A01065346).

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Invariant subspace
Unitary weighted composition operator
Weighted composition operator

Access to Document

10.1007/s11785-021-01193-5

Cite this

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abstract = "In this paper we study the square roots of unitary weighted composition operators on the Hardy space H2, i.e., Wf,φ when Wg,ψ=Wf,φ2 is unitary. In particular, we provide the explicit forms of the symbol functions φ and f of such Wf,φ. Moreover, we show that the square roots Wf,φ of a unitary weighted composition operator are normal. Finally, we investigate several properties of such Wf,φ.",

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