<i>C</i>*-module operators which satisfy the generalized Cauchy–Schwarz type inequality

نویسندگان

چکیده

Let L(H) denote the C∗-algebra of adjointable operators on a Hilbert C∗-module H. In this paper, we introduce generalized Cauchy–Schwarz inequality for in L(H). More precisely, an operator A∈L(H) is said to satisfy if there exists ν∈(0,1) such that ‖⟨Ax,y⟩‖≤(‖Ax‖‖y‖)ν(‖Ay‖‖x‖)1−ν(x,y∈H).We investigate various properties which inequality. particular, prove A satisfies has polar decomposition, then paranormal. addition, show equality holds inequality, cohyponormal. Among other things, when semi-hyponormal and only ‖⟨Ax,y⟩‖≤‖|A|1/2x‖‖|A|1/2y‖ all x,y∈H.

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ژورنال

عنوان ژورنال: Linear & Multilinear Algebra

سال: 2022

ISSN: ['0308-1087', '1026-7573', '1563-5139']

DOI: https://doi.org/10.1080/03081087.2022.2160862