Properties of $C$-normal operators (Research on preserver problems on Banach algebras and related topics)

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Abstract

We study various properties of $C$-normal operators, i.e., $T*T$ = $CTT*C$ holds for a conjugation $C$ on $H$. Especially, we show that $T$ − λ$I$ is $C$-normal for all λ ∈ ℂ if and only if $T$ is a complex symmetric operator with the conjugation $C$. In addition, we prove that if $T$ is $C$-normal, then $T$ is normal ⇔ $T$ is quasinormal ⇔ $T$ is hyponormal ⇔ $T$ is $p$-hyponormal for 0 < $p$ ≤ 1. Finally, we investigate equivalent conditions so that Aluthge and Duggal transforms of $C$-normal operators to be $C$-normal operators.

Journal

  • RIMS Kokyuroku Bessatsu

    RIMS Kokyuroku Bessatsu B93 117-124, 2023-07

    Research Institute for Mathematical Sciences, Kyoto University

Keywords

Details 詳細情報について

  • CRID
    1050015897173947392
  • NII Book ID
    AA12196120
  • HANDLE
    2433/284874
  • ISSN
    18816193
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • IRDB

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