An Infinite Transitivity Theorem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914270370856960 |
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| author | Gould, Miles |
| author_facet | Gould, Miles |
| contents | In this note, we promote an infinite Kadison transitivity theorem on massive $C^*$-algebras, including the Calkin algebra. This transitivity stems from the analog of countable degree-1 saturation on pure states which is inherited from these algebras via excision. We show this saturation to be equivalent to several order-theoretic properties on the quantum filter associated to the state, in particular the property of being a quantum P-point. While we show their existence is independent from ZFC, under basic set theoretic assumptions, we produce a plethora of these states. Finally, we find an irreducible representation of the Calkin algebra which fails infinite transitivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07549 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Infinite Transitivity Theorem Gould, Miles Operator Algebras 46L05 In this note, we promote an infinite Kadison transitivity theorem on massive $C^*$-algebras, including the Calkin algebra. This transitivity stems from the analog of countable degree-1 saturation on pure states which is inherited from these algebras via excision. We show this saturation to be equivalent to several order-theoretic properties on the quantum filter associated to the state, in particular the property of being a quantum P-point. While we show their existence is independent from ZFC, under basic set theoretic assumptions, we produce a plethora of these states. Finally, we find an irreducible representation of the Calkin algebra which fails infinite transitivity. |
| title | An Infinite Transitivity Theorem |
| topic | Operator Algebras 46L05 |
| url | https://arxiv.org/abs/2512.07549 |