On operators T commuting with CTC where C is a conjugation

Muneo Chō, Eungil Ko, Ji Eun Lee

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)69-79
Number of pages11
JournalBulletin of the Korean Mathematical Society
Volume57
Issue number1
DOIs
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 Korean Mathematical Society.

Keywords

  • Complex symmetric operator
  • Conjugation operator
  • Normal operator

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