Operator convex functions of several variables

DOI10.2977/prims/1195145324zbMath0902.47013OpenAlexW2074082380MaRDI QIDQ1378353

Frank Hansen

Publication date: 16 June 1998

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195145324

zbMATH Keywords

tensor productfunctional calculus for functions of several variablesgeneralized Hessian matricessecond Fréchet differential

Mathematics Subject Classification ID

Functional calculus for linear operators (47A60) Miscellaneous inequalities involving matrices (15A45)

Related Items (18)

A dual formula for the noncommutative transport distance ⋮ Trace functions as Laplace transforms ⋮ On differentiability of a class of orthogonally invariant functions on several operator variables ⋮ More on operator monotone and operator convex functions of several variables ⋮ The fast track to Löwner's theorem ⋮ Non-commutative polynomial solutions to partial differential equations ⋮ Extensions of Lieb's concavity theorem ⋮ Hermite-Hadamard type inequalities for operator convex functions on the co-ordinates ⋮ On the analyticity of k-isotropic functions ⋮ Hermite-Hadamard type inequalities for functions whose derivatives are operator convex ⋮ The Hessian of a noncommutative polynomial has numerous negative eigenvalues ⋮ Operator differentiable functions ⋮ Monotone matrix functions of two variables ⋮ Order generalised gradient and operator inequalities ⋮ DUAL GEOMETRY OF THE WIGNER–YANASE–DYSON INFORMATION CONTENT ⋮ Convex trace functions of several variables. ⋮ Some operator convex functions of several variables ⋮ Jensen's Trace Inequality in Several Variables

Cites Work

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• Über monotone Matrixfunktionen
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• Über konvexe Matrixfunktionen
• Significance of Loewner's theorem in the quantum theory of collisions
• On Some Classes of Analytic Functions of Several Variables
• Jensen’s operator inequality for functions of two variables
• The calculus of operator functions and operator convexity
• Expansional in banach algebras
• Monotone and Convex Operator Functions
• An operator inequality

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