Loewner’s theorem for maps on operator domains

DOI10.4153/s0008414x22000219zbMath1529.47072arXiv2006.04488OpenAlexW3032961357WikidataQ113692058 ScholiaQ113692058MaRDI QIDQ6041839

Peter Šemrl, Michiya Mori

Publication date: 15 May 2023

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.04488

zbMATH Keywords

Loewner's theoremorder embeddingbiholomorphic mapgeneralized upper half-planeoperator domainlocal order isomorphism

Mathematics Subject Classification ID

Infinite-dimensional holomorphy (46G20) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Linear operators on ordered spaces (47B60) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Cites Work

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• Comparability preserving maps on Hilbert space effect algebras
• Free Pick functions: representations, asymptotic behavior and matrix monotonicity in several noncommuting variables
• Selected preserver problems on algebraic structures of linear operators and on function spaces
• Means of positive linear operators
• Order isomorphisms of operator intervals
• Operator monotone functions and Löwner functions of several variables
• Positive linear maps of operator algebras
• Significance of Loewner's theorem in the quantum theory of collisions
• Order-automorphisms of the set of bounded observables
• Loewner's Theorem on Monotone Matrix Functions
• Book Review: Loewner’s theorem on monotone matrix functions

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