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On properties of C-normal operators

Title
On properties of C-normal operators
Authors
Ko, EungilLee, Ji EunLee, Mee-Jung
Ewha Authors
고응일이미정
SCOPUS Author ID
고응일scopus; 이미정scopusscopus
Issue Date
2021
Journal Title
BANACH JOURNAL OF MATHEMATICAL ANALYSIS
ISSN
2662-2033JCR Link

1735-8787JCR Link
Citation
BANACH JOURNAL OF MATHEMATICAL ANALYSIS vol. 15, no. 4
Keywords
C-normal operatorComplex symmetric operatorOperator transforms
Publisher
SPRINGER BASEL AG
Indexed
SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
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.
DOI
10.1007/s43037-021-00147-5
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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