On the generalized mean transforms of complex symmetric operators

Chafiq Benhida; Muneo Chō; Eungil Ko; Ji Eun Lee

doi:10.1007/s43037-019-00041-1

On the generalized mean transforms of complex symmetric operators

Chafiq Benhida, Muneo Chō, Eungil Ko, Ji Eun Lee

Department of Mathematics

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

4 Scopus citations

Abstract

In this paper, we prove that if T∈ L(H) is complex symmetric, then its generalized mean transform T^(t)(t≠0) of T is also complex symmetric. Next, we consider complex symmetry property of the mean transform T^ (0) of truncated weighted shift operators. Finally, we study properties of the generalized mean transform of skew complex symmetric operators.

Original language	English
Pages (from-to)	842-855
Number of pages	14
Journal	Banach Journal of Mathematical Analysis
Volume	14
Issue number	3
DOIs	https://doi.org/10.1007/s43037-019-00041-1
State	Published - 1 Jul 2020

Bibliographical note

Funding Information:
The authors wish to thank the referees for their invaluable comments on the original draft. C. Benhida was partially supported by Labex CEMPI (ANR-11-LABX-0007-01). M. Chō is partially supported by Grant-in-Aid Scientific Research no. 15K04910. E. Ko was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1F1A1058633). J. E. Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1A2C1002653).

Publisher Copyright:
© 2019, Tusi Mathematical Research Group (TMRG).

Keywords

Complex symmetric operator
Generalized mean transform
Skew-complex symmetric operator

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10.1007/s43037-019-00041-1

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abstract = "In this paper, we prove that if T∈ L(H) is complex symmetric, then its generalized mean transform T^(t)(t≠0) of T is also complex symmetric. Next, we consider complex symmetry property of the mean transform T^ (0) of truncated weighted shift operators. Finally, we study properties of the generalized mean transform of skew complex symmetric operators.",

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author = "Chafiq Benhida and Muneo Chō and Eungil Ko and Lee, {Ji Eun}",

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doi = "10.1007/s43037-019-00041-1",

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AU - Chō, Muneo

AU - Ko, Eungil

AU - Lee, Ji Eun

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N2 - In this paper, we prove that if T∈ L(H) is complex symmetric, then its generalized mean transform T^(t)(t≠0) of T is also complex symmetric. Next, we consider complex symmetry property of the mean transform T^ (0) of truncated weighted shift operators. Finally, we study properties of the generalized mean transform of skew complex symmetric operators.

AB - In this paper, we prove that if T∈ L(H) is complex symmetric, then its generalized mean transform T^(t)(t≠0) of T is also complex symmetric. Next, we consider complex symmetry property of the mean transform T^ (0) of truncated weighted shift operators. Finally, we study properties of the generalized mean transform of skew complex symmetric operators.

KW - Complex symmetric operator

KW - Generalized mean transform

KW - Skew-complex symmetric operator

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JO - Banach Journal of Mathematical Analysis

JF - Banach Journal of Mathematical Analysis

IS - 3

ER -

On the generalized mean transforms of complex symmetric operators

Abstract

Bibliographical note

Keywords

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