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- W4313396983 abstract "Let L(H) denote the C∗-algebra of adjointable operators on a Hilbert C∗-module H. In this paper, we introduce the generalized Cauchy–Schwarz inequality for operators in L(H). More precisely, an operator A∈L(H) is said to satisfy the generalized Cauchy–Schwarz inequality if there exists ν∈(0,1) such that ‖⟨Ax,y⟩‖≤(‖Ax‖‖y‖)ν(‖Ay‖‖x‖)1−ν(x,y∈H).We investigate various properties of operators which satisfy the generalized Cauchy–Schwarz inequality. In particular, we prove that if A satisfies the generalized Cauchy–Schwarz inequality such that A has the polar decomposition, then A is paranormal. In addition, we show that if for A the equality holds in the generalized Cauchy–Schwarz inequality, then A is cohyponormal. Among other things, when A has the polar decomposition, we prove that A is semi-hyponormal if and only if ‖⟨Ax,y⟩‖≤‖|A|1/2x‖‖|A|1/2y‖ for all x,y∈H." @default.
- W4313396983 created "2023-01-06" @default.
- W4313396983 creator A5012614401 @default.
- W4313396983 date "2022-12-31" @default.
- W4313396983 modified "2023-10-14" @default.
- W4313396983 title "<i>C</i>*-module operators which satisfy the generalized Cauchy–Schwarz type inequality" @default.
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- W4313396983 doi "https://doi.org/10.1080/03081087.2022.2160862" @default.
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