On operators satisfying the generalized Cauchy-Schwarz inequality

Hanna Choi, Yoenha Kim, Eungil Ko

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish
Pages (from-to)3447-3453
Number of pages7
JournalProceedings of the American Mathematical Society
Volume145
Issue number8
DOIs
StatePublished - 2017

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