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자연과학대학
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On operators satisfying the generalized Cauchy-Schwarz inequality
Title
On operators satisfying the generalized Cauchy-Schwarz inequality
Authors
Choi H.
;
Kim Y.
;
Ko E.
Ewha Authors
고응일
;
김연하
SCOPUS Author ID
고응일
; 김연하
Issue Date
2017
Journal Title
Proceedings of the American Mathematical Society
ISSN
0002-9939
Citation
Proceedings of the American Mathematical Society vol. 145, no. 8, pp. 3447 - 3453
Publisher
American Mathematical Society
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
In this paper, we introduce the generalized Cauchy-Schwarz inequality for an operator T ∈ L(H) and investigate various properties of operators which satisfy the generalized Cauchy-Schwarz inequality. In particular, every p-hyponormal operator satisfies this inequality. We also prove that if T ∈ L(H) satisfies the generalized Cauchy-Schwarz inequality, then T is paranormal. As an application, we show that if both T and T∗ in L(H) satisfy the generalized Cauchy-Schwarz inequality, then T is normal. © 2017 American Mathematical Society.
DOI
10.1090/proc/13473
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