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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.00121 |
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| _version_ | 1866914075030585344 |
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| author | Healey, Curt |
| author_facet | Healey, Curt |
| contents | 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 Löwner's theorem and our aim is to provide a comprehensive review of one of the proofs of Löwner'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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a comprehensive review of a proof of Löwner's theorem Healey, Curt Functional Analysis Operator Algebras 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 Löwner's theorem and our aim is to provide a comprehensive review of one of the proofs of Löwner'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. |
| title | On a comprehensive review of a proof of Löwner's theorem |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2510.00121 |