A new majorization between functions, polynomials, and operator inequalities

DOI10.1016/j.jfa.2005.03.005zbMath1102.47010OpenAlexW2047582927MaRDI QIDQ2368773

Mitsuru Uchiyama

Publication date: 28 April 2006

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2005.03.005

zbMATH Keywords

operator monotone functionLöwner-Heinz inequalitymajorizationPick functionorthogonal polynomialmatrix order

Mathematics Subject Classification ID

Linear operator inequalities (47A63)

Related Items (15)

Some results on strongly operator convex functions and operator monotone functions ⋮ Majorization and some operator monotone functions ⋮ Geometric convexity of an operator mean ⋮ A new family of weighted operator means including the weighted Heron, logarithmic and Heinz means ⋮ Comprehensive survey on an order preserving operator inequality ⋮ From Schoenberg to Pick-Nevanlinna: toward a complete picture of the variogram class ⋮ Operator inequalities: from a general theorem to concrete inequalities ⋮ A new majorization between functions, polynomials, and operator inequalities. II ⋮ A Converse of the Loewner–Heinz Inequality, Geometric Mean and Spectral Order ⋮ Operator monotone functions, positive definite kernels and majorization ⋮ Inequalities for generalized derivations of operator monotone functions in norm ideals of compact operators ⋮ A New Majorization Induced by Matrix Order ⋮ Nonhomogeneous Karcher equations with vector fields on positive definite matrices ⋮ A family of weighted operator means including the weighted Heinz and Lehmer means ⋮ Interpolation functions and inequalities

Cites Work

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• Jensen's inequality for operators and Loewner's theorem
• Criteria for monotonicity of operator means.
• Operator monotone functions which are defined implicitly and operator inequalities
• Comparison of norms \(|||f(A)-f(B)|||\) and \(|||f(|A-B|)|||\)
• Some exponential operator inequalities
• Inverse functions of polynomials and orthogonal polynomials as operator monotone functions
• Best possibility of the Furuta inequality
• $A \geq B \geq 0$ Assures $(B^r A^p B^r)^{1/q} \geq B^{(p+2r)/q$ for $r \geq 0$, $p \geq 0$, $q \geq 1$ with $(1 + 2r)q \geq p + 2r$
• On some operator inequalities
• Mixed matrix (operator) inequalities
• On some operator monotone functions

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