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ON OPERATORS SATISFYING THE GENERALIZED CAUCHY-SCHWARZ INEQUALITY
- ON OPERATORS SATISFYING THE GENERALIZED CAUCHY-SCHWARZ INEQUALITY
- Choi, Hanna; Kim, Yoenha; Ko, Eungil
- Ewha Authors
- 고응일; 김연하
- SCOPUS Author ID
- Issue Date
- Journal Title
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
- 0002-9939; 1088-6826
- vol. 145, no. 8, pp. 3447 - 3453
- AMER MATHEMATICAL SOC
- SCI; SCIE; SCOPUS
- In this paper, we introduce the generalized Cauchy-Schwarz inequality for an operator T is an element of 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 is an element of 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.
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