Contractivity and expansivity of H-Toeplitz operators on the Bergman spaces

Sumin Kim; Jongrak Lee; Sumin Kim; Jongrak Lee

doi:10.3934/math.2022769

AIMS Mathematics

2022, Volume 7, Issue 8: 13927-13944. doi: 10.3934/math.2022769

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Research article

Contractivity and expansivity of H-Toeplitz operators on the Bergman spaces

Sumin Kim ¹,
Jongrak Lee ^{2
,
,}

1.
Department of Mathematics and Research Institute of Natural Sciences, Hanyang University, Seoul 04763, Korea
2.
Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea

Received: 24 March 2022 Revised: 10 May 2022 Accepted: 16 May 2022 Published: 25 May 2022
MSC : 47B35, 46E20

In this paper we consider the properties of H-Toeplitz operators $ B_{\varphi} $ on the Bergman space $ L^2_a(\Bbb D) $. We present some necessary and sufficient conditions for the contractive and expansive H-Toeplitz operators $ B_\varphi $ with various symbols $ \varphi $.
- H-Toeplitz operators,
- contractive operators,
- expansive operators,
- Bergman space
Citation: Sumin Kim, Jongrak Lee. Contractivity and expansivity of H-Toeplitz operators on the Bergman spaces[J]. AIMS Mathematics, 2022, 7(8): 13927-13944. doi: 10.3934/math.2022769

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Abstract

In this paper we consider the properties of H-Toeplitz operators $ B_{\varphi} $ on the Bergman space $ L^2_a(\Bbb D) $. We present some necessary and sufficient conditions for the contractive and expansive H-Toeplitz operators $ B_\varphi $ with various symbols $ \varphi $.

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