@article{ee2ba043b6bd465cb108001f694e99eb,

title = "On operators satisfying the generalized Cauchy-Schwarz inequality",

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.",

author = "Hanna Choi and Yoenha Kim and Eungil Ko",

note = "Funding Information: This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2015R1C1A1A02036456). Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

year = "2017",

doi = "10.1090/proc/13473",

language = "English",

volume = "145",

pages = "3447--3453",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "8",

}