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On properties of C-normal operators
- On properties of C-normal operators
- Ko, Eungil; Lee, Ji Eun; Lee, Mee-Jung
- Ewha Authors
- 고응일; 이미정
- SCOPUS Author ID
- 고응일; 이미정
- Issue Date
- Journal Title
- BANACH JOURNAL OF MATHEMATICAL ANALYSIS
- BANACH JOURNAL OF MATHEMATICAL ANALYSIS vol. 15, no. 4
- C-normal operator; Complex symmetric operator; Operator transforms
- SPRINGER BASEL AG
- SCIE; SCOPUS
- Document Type
- A bounded linear operator T:H -> H is a C-normal operator if there exists a conjugation C on H such that [CT,(CT)*]=0 where [R,S]:=RS-SR. In this paper we study properties of C-normal operators. In particular, we prove that T-lambda is C-normal for all lambda is an element of C if and only if T is a complex symmetric operator with the conjugation C. Moreover, we show that if T is C-normal, then the following statements are equivalent; (i) T is normal, (ii) T is quasinormal, (iii) T is hyponormal, (iv) T is p-hyponormal for 0 < p <= 1. Finally, we consider operator transforms of C-normal operators.
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