A treatment of the Cauchy-Schwarz inequality in \(C^{*}\)-modules

DOI10.1016/j.jmaa.2011.02.062zbMath1225.46045arXiv0905.3509OpenAlexW2963598469MaRDI QIDQ542827

Mohammad Sal Moslehian, Ljiljana Arambašić, Damir Bakić

Publication date: 20 June 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.3509

zbMATH Keywords

\(C^*\)-algebraOstrowski inequalitypositive operatorGram matrixCauchy-Schwarz inequalitycovariance-variance inequalitysemi-inner product \(C^*\)-module

Mathematics Subject Classification ID

(C^*)-modules (46L08)

Related Items (18)

Some bounds for central moments and spreads of matrices ⋮ Similarities and differences between real and complex Banach spaces: an overview and recent developments ⋮ Cauchy–Schwarz Operator and Norm Inequalities for Inner Product Type Transformers in Norm Ideals of Compact Operators, with Applications ⋮ Continuity of positive nonlinear maps between $C^*$-algebras ⋮ Conditionally positive definite kernels in Hilbert \(C^*\)-modules ⋮ Operator inequalities of Hölder type for unitarily invariant norms ⋮ Recent developments of the operator Kantorovich inequality ⋮ Refinements of the Cauchy-Schwarz inequality in pre-Hilbert \(C^\ast\)-modules and their applications ⋮ Non-commutative Callebaut inequality ⋮ Bounds on spreads of matrices related to fourth central moment ⋮ Matrix inequalities related to Hölder inequality ⋮ C *-module operators which satisfy the generalized Cauchy–Schwarz type inequality ⋮ Cauchy-Schwarz inequality in semi-inner product \(C^{\ast}\)-modules via polar decomposition ⋮ Some reversed and refined Callebaut inequalities via Kantorovich constant ⋮ Noncommutative versions of inequalities in quantum information theory ⋮ Vector-valued reproducing kernel Hilbert \(C^*\)-modules ⋮ Complementary and refined inequalities of Callebaut inequality for operators ⋮ Inequalities for central moments and spreads of matrices

Cites Work

• Operator-valued inner product and operator inequalities
• Operator inequalities related to Cauchy-Schwarz and Hölder-McCarthy inequalities
• On the Cauchy-Schwarz inequality and its reverse in semi-inner product \(C^*\)-modules
• Reverse Cauchy--Schwarz inequalities for positive C^✻-valued sesquilinear forms
• More operator versions of the Schwarz inequality
• Theory of operator algebras I.
• On variance and covariance for bounded linear operators
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