On properties of C-normal operators II

Eungil Ko, Ji Eun Lee, Mee Jung Lee

Research output: Contribution to journalArticlepeer-review

Abstract

For T∈ L(H) , an operator T is called C-normal if (CT) #CT= CT(CT) # for a conjugation C on H. In this paper, we continue our study, begun in Ko et al. (Banach J. Math. Anal. 14:1711–1727, 2020), of various properties of C-normal operators. Especially, we prove that if T= U| T| is the polar decomposition of T, C is a conjugation on H with UCU= C, and T is C-normal, then T possess the property (β) , the single valued extension property, the property (C) if and only if T possess, respectively. In addition, if T is C-normal, then T is binormal if and only if | T| n and C| T| mC commute for everyl positive integers m, n.

Original languageEnglish
Article number29
JournalAnnals of Functional Analysis
Volume14
Issue number2
DOIs
StatePublished - Apr 2023

Bibliographical note

Publisher Copyright:
© 2023, Tusi Mathematical Research Group (TMRG).

Keywords

  • Binormal
  • C-normal operator
  • The property (C)
  • The property (β)

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