Characterizations of Square Roots of Unitary Weighted Composition Operators on H2

Yoenha Kim, Eungil Ko

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2 Scopus citations

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.

Original languageEnglish
Article number14
JournalComplex Analysis and Operator Theory
Volume16
Issue number1
DOIs
StatePublished - 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

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