Non-linear traces of Choquet type on AF algebras
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911415946706944 |
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| author | Ninomiya, Ryota |
| author_facet | Ninomiya, Ryota |
| contents | We study non-linear traces of Choquet type on AF algebras. Building on the characterization of Choquet traces on matrix algebras due to Nagisa--Watatani, we generalize the construction to arbitrary unital AF algebras. We show that there is a one-to-one correspondence between such traces and increasing functions on the dimension scale, and we obtain explicit Choquet formulas in terms of the spectrum and ranks of spectral projections along a fixed AF filtration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14016 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-linear traces of Choquet type on AF algebras Ninomiya, Ryota Operator Algebras 28A25, 46L05 We study non-linear traces of Choquet type on AF algebras. Building on the characterization of Choquet traces on matrix algebras due to Nagisa--Watatani, we generalize the construction to arbitrary unital AF algebras. We show that there is a one-to-one correspondence between such traces and increasing functions on the dimension scale, and we obtain explicit Choquet formulas in terms of the spectrum and ranks of spectral projections along a fixed AF filtration. |
| title | Non-linear traces of Choquet type on AF algebras |
| topic | Operator Algebras 28A25, 46L05 |
| url | https://arxiv.org/abs/2601.14016 |