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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.21873 |
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| _version_ | 1866917518304608256 |
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| author | Ando, Hiroshi Goldbring, Isaac |
| author_facet | Ando, Hiroshi Goldbring, Isaac |
| contents | We prove, for any W$^*$-probability space $(M,φ)$ where $M$ is a type $\mathrm{III}_1$ factor, any nontrivial, proper closed $F\subseteq \mathbb{R}$, and any nonprincipal ultrafilter $\mathcal{U}$ on $\mathbb{N}$, that the ultrapower $M(σ^φ,F)^{\mathcal{U}}$ of the spectral subspace $M(σ^φ,F)$ is a proper subset of the spectral subspace $M^{\mathcal{U}}(σ^{φ^{\mathcal{U}}},F)$. We discuss the model-theoretic implications of this result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21873 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ultrapowers of spectral subspaces Ando, Hiroshi Goldbring, Isaac Operator Algebras Logic We prove, for any W$^*$-probability space $(M,φ)$ where $M$ is a type $\mathrm{III}_1$ factor, any nontrivial, proper closed $F\subseteq \mathbb{R}$, and any nonprincipal ultrafilter $\mathcal{U}$ on $\mathbb{N}$, that the ultrapower $M(σ^φ,F)^{\mathcal{U}}$ of the spectral subspace $M(σ^φ,F)$ is a proper subset of the spectral subspace $M^{\mathcal{U}}(σ^{φ^{\mathcal{U}}},F)$. We discuss the model-theoretic implications of this result. |
| title | Ultrapowers of spectral subspaces |
| topic | Operator Algebras Logic |
| url | https://arxiv.org/abs/2605.21873 |