On properties of C-normal operators
- 주제(키워드) C-normal operator , Complex symmetric operator , Operator transforms
- 주제(기타) Mathematics, Applied; Mathematics
- 설명문(일반) [Ko, Eungil] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea; [Lee, Ji Eun] Sejong Univ, Dept Math & Stat, Seoul 05006, South Korea; [Lee, Mee-Jung] Ewha Womans Univ, Inst Math Sci, Seoul 03760, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 SPRINGER BASEL AG
- 발행년도 2021
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000183544
- 본문언어 영어
- Published As http://dx.doi.org/10.1007/s43037-021-00147-5
초록/요약
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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