Operators on anti-dual pairs: Lebesgue decomposition via Arlinskii's iteration
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909322002300928 |
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| author | Göde, Ábel Tarcsay, Zsigmond |
| author_facet | Göde, Ábel Tarcsay, Zsigmond |
| contents | The aim of this paper is to prove a general Lebesgue decomposition theorem for positive operators on so-called anti-dual pairs, following the iterative approach introduced by Arlinskii. This procedure and the resulting theorem encompass several special cases, including positive operators on Hilbert spaces, non-negative forms on vector spaces, and representable functionals over *-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14068 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operators on anti-dual pairs: Lebesgue decomposition via Arlinskii's iteration Göde, Ábel Tarcsay, Zsigmond Functional Analysis 47B65, 47A07 The aim of this paper is to prove a general Lebesgue decomposition theorem for positive operators on so-called anti-dual pairs, following the iterative approach introduced by Arlinskii. This procedure and the resulting theorem encompass several special cases, including positive operators on Hilbert spaces, non-negative forms on vector spaces, and representable functionals over *-algebras. |
| title | Operators on anti-dual pairs: Lebesgue decomposition via Arlinskii's iteration |
| topic | Functional Analysis 47B65, 47A07 |
| url | https://arxiv.org/abs/2409.14068 |