Cauchy-Schwarz inequality in semi-inner product \(C^{\ast}\)-modules via polar decomposition

DOI10.1016/j.jmaa.2012.04.083zbMath1257.46026OpenAlexW2111257541MaRDI QIDQ442513

Mohammad Sal Moslehian, Yuki Seo, Masatoshi Fujii, Jun Ichi Fujii

Publication date: 1 August 2012

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.04.083

zbMATH Keywords

operator inequalitypositive operatorKantorovich inequalityoperator geometric meanHilbert \(C^{\ast }\)-module

Mathematics Subject Classification ID

Linear operator inequalities (47A63) (C^*)-modules (46L08) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (11)

Cauchy–Schwarz Operator and Norm Inequalities for Inner Product Type Transformers in Norm Ideals of Compact Operators, with Applications ⋮ Reverse Schwarz inequalities and some consequences in inner product spaces ⋮ 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 ⋮ Matrix inequalities related to Hölder inequality ⋮ Norm-parallelism in the geometry of Hilbert \(C^\ast\)-modules ⋮ A Grüss type inequality for vector-valued functions in Hilbert \(C^*\)-modules ⋮ Unnamed Item ⋮ On reverse Schwarz, Bessel, Grüss and Hadamard inequalities in inner product spaces ⋮ Equality conditions of reverse Schwarz and Grüss inequalities in inner productspaces

Cites Work

• Bessel and Grüss type inequalities in inner product modules over Banach \(\ast \)-algebras
• A treatment of the Cauchy-Schwarz inequality in \(C^{*}\)-modules
• On some refinement of the Cauchy--Schwarz inequality
• Operator-valued inner product and operator inequalities
• Functional calculus for sesquilinear forms and the purification map
• Means of positive linear operators
• Operator inequalities related to Cauchy-Schwarz and Hölder-McCarthy inequalities
• On the Cauchy-Schwarz inequality and its reverse in semi-inner product \(C^*\)-modules
• An extension of Kantorovich inequality to \(n\)-operators via the geometric mean by Ando--Li--Mathias
• Reverse Cauchy--Schwarz inequalities for positive C^✻-valued sesquilinear forms
• Unified treatment of complemented Schwarz and Grüss inequalities in inner product spaces
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