On operators T commuting with CTC where C is a conjugation

Muneo Chō; Eungil Ko; Ji Eun Lee

doi:10.4134/BKMS.b190054

On operators T commuting with CTC where C is a conjugation

Muneo Chō, Eungil Ko, Ji Eun Lee

Department of Mathematics

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

2 Scopus citations

Abstract

In this paper, we study the properties of T satisfying [CT C, T ] = 0 for some conjugation C where [R, S]:= RS − SR. In particular, we show that if T is normal, then [CT C, C] = 0. Moreover, the class of operators T satisfy [CT C, T ] = 0 is norm closed. Finally, we prove that if T is complex symmetric, then T is binormal if and only if [C|T |C, |T |] = 0.

Original language	English
Pages (from-to)	69-79
Number of pages	11
Journal	Bulletin of the Korean Mathematical Society
Volume	57
Issue number	1
DOIs	https://doi.org/10.4134/BKMS.b190054
State	Published - 2020

Bibliographical note

Publisher Copyright:
© 2020 Korean Mathematical Society.

Keywords

Complex symmetric operator
Conjugation operator
Normal operator

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abstract = "In this paper, we study the properties of T satisfying [CT C, T ] = 0 for some conjugation C where [R, S]:= RS − SR. In particular, we show that if T is normal, then [CT C, C] = 0. Moreover, the class of operators T satisfy [CT C, T ] = 0 is norm closed. Finally, we prove that if T is complex symmetric, then T is binormal if and only if [C|T |C, |T |] = 0.",

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AU - Ko, Eungil

AU - Lee, Ji Eun

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AB - In this paper, we study the properties of T satisfying [CT C, T ] = 0 for some conjugation C where [R, S]:= RS − SR. In particular, we show that if T is normal, then [CT C, C] = 0. Moreover, the class of operators T satisfy [CT C, T ] = 0 is norm closed. Finally, we prove that if T is complex symmetric, then T is binormal if and only if [C|T |C, |T |] = 0.

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KW - Conjugation operator

KW - Normal operator

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On operators T commuting with CTC where C is a conjugation

Abstract

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Keywords

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