Properties of $C$-normal operators (Research on preserver problems on Banach algebras and related topics)
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- KO, Eungil
- Department of Mathematics, Ewha Womans University
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- LEE, Ji Eun
- Department of Mathematics and Statistics, Sejong University
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- LEE, Mee-Jung
- College of General Education, Kookmin University
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抄録
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.
収録刊行物
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- 数理解析研究所講究録別冊
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数理解析研究所講究録別冊 B93 117-124, 2023-07
Research Institute for Mathematical Sciences, Kyoto University
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詳細情報 詳細情報について
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- CRID
- 1050015897173947392
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- NII書誌ID
- AA12196120
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- HANDLE
- 2433/284874
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- ISSN
- 18816193
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- 本文言語コード
- en
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- 資料種別
- departmental bulletin paper
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- データソース種別
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- IRDB