Conjugations and Complex Symmetric Toeplitz Operators on the Weighted Hardy Space

Eungil Ko; Ji Eun Lee; Jongrak Lee

doi:10.1007/s00009-021-01754-0

Conjugations and Complex Symmetric Toeplitz Operators on the Weighted Hardy Space

Eungil Ko, Ji Eun Lee, Jongrak Lee

Department of Mathematics

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

1 Scopus citations

Abstract

In this paper, we introduce a new conjugation C_ξ on the weighted Hardy space H_ρ(D) , where C_ξ is given by (2.1) in Theorem 2.2. In particular, we prove that C_ξ and C_μ_,_λ are unitarily equivalent where C_μ_,_λ is given in Ko and Lee (J Math Anal Appl 434:20–34, 2016). Using this, we investigate a complex symmetric Toeplitz operator T_φ with respect to the conjugation C_ξ on the weighted Hardy space H_ρ(D). Finally, we consider C_μ_,_λ-invariant of Berezin transform.

Original language	English
Article number	125
Journal	Mediterranean Journal of Mathematics
Volume	18
Issue number	4
DOIs	https://doi.org/10.1007/s00009-021-01754-0
State	Published - Aug 2021

Bibliographical note

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

Keywords

Conjugation
Toeplitz operator
complex symmetric operator
weighted Hardy space

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title = "Conjugations and Complex Symmetric Toeplitz Operators on the Weighted Hardy Space",

abstract = "In this paper, we introduce a new conjugation Cξ on the weighted Hardy space Hρ(D) , where Cξ is given by (2.1) in Theorem 2.2. In particular, we prove that Cξ and Cμ,λ are unitarily equivalent where Cμ,λ is given in Ko and Lee (J Math Anal Appl 434:20–34, 2016). Using this, we investigate a complex symmetric Toeplitz operator Tφ with respect to the conjugation Cξ on the weighted Hardy space Hρ(D). Finally, we consider Cμ,λ-invariant of Berezin transform.",

keywords = "Conjugation, Toeplitz operator, complex symmetric operator, weighted Hardy space",

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AU - Ko, Eungil

AU - Lee, Ji Eun

AU - Lee, Jongrak

PY - 2021/8

Y1 - 2021/8

N2 - In this paper, we introduce a new conjugation Cξ on the weighted Hardy space Hρ(D) , where Cξ is given by (2.1) in Theorem 2.2. In particular, we prove that Cξ and Cμ,λ are unitarily equivalent where Cμ,λ is given in Ko and Lee (J Math Anal Appl 434:20–34, 2016). Using this, we investigate a complex symmetric Toeplitz operator Tφ with respect to the conjugation Cξ on the weighted Hardy space Hρ(D). Finally, we consider Cμ,λ-invariant of Berezin transform.

AB - In this paper, we introduce a new conjugation Cξ on the weighted Hardy space Hρ(D) , where Cξ is given by (2.1) in Theorem 2.2. In particular, we prove that Cξ and Cμ,λ are unitarily equivalent where Cμ,λ is given in Ko and Lee (J Math Anal Appl 434:20–34, 2016). Using this, we investigate a complex symmetric Toeplitz operator Tφ with respect to the conjugation Cξ on the weighted Hardy space Hρ(D). Finally, we consider Cμ,λ-invariant of Berezin transform.

KW - Conjugation

KW - Toeplitz operator

KW - complex symmetric operator

KW - weighted Hardy space

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SN - 1660-5446

VL - 18

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 4

M1 - 125

ER -

Conjugations and Complex Symmetric Toeplitz Operators on the Weighted Hardy Space

Abstract

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Keywords

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