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arXiv · 2510.00121

On a comprehensive review of a proof of L\"owner's theorem

Curt Healey
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Abstract

Recent studies in Kubo-Ando theory make frequent use of the relationship between Kubo-Ando connections and positive operator monotone functions. This relationship is deeply connected to L\"owner's theorem and our aim is to provide a comprehensive review of one of the proofs of L\"owner's theorem. Our motivation arises from the fact that the foundational components upon which the theorem rests are found within a variety of sources, rendering it difficult to obtain a complete understanding of the proof without engaging in substantial external consultation. By consolidating these elements into a single, continuous account, the proof becomes substantially more accessible and may be assimilated with greater clarity and efficiency.

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Curt Healey. 2025-09-30. On a comprehensive review of a proof of L\"owner's theorem. https://arxiv.org/abs/2510.00121

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