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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.01481 |
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| _version_ | 1866913678190706688 |
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| author | Dhahri, Ameur Ko, Chul Ki Yoo, Hyun Jae |
| author_facet | Dhahri, Ameur Ko, Chul Ki Yoo, Hyun Jae |
| contents | For a $*$-automorphism group $G$ on a $C^*$- or von Neumann algebra, we study the $G$-quasi invariant states and their properties. The $G$-quasi invariance or $G$-strongly quasi invariance are weaker than the $G$-invariance and have wide applications. We develop several properties for $G$-strongly quasi invariant states. Many of them are the extensions of the already developed theories for $G$-invariant states. Among others, we consider the relationship between the group $G$ and modular automorphism group, invariant subalgebras, ergodicity, modular theory, and abelian subalgebras. We provide with some examples to support the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01481 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Group of automorphisms for strongly quasi invariant states Dhahri, Ameur Ko, Chul Ki Yoo, Hyun Jae Operator Algebras Mathematical Physics 37N20, 81P16 For a $*$-automorphism group $G$ on a $C^*$- or von Neumann algebra, we study the $G$-quasi invariant states and their properties. The $G$-quasi invariance or $G$-strongly quasi invariance are weaker than the $G$-invariance and have wide applications. We develop several properties for $G$-strongly quasi invariant states. Many of them are the extensions of the already developed theories for $G$-invariant states. Among others, we consider the relationship between the group $G$ and modular automorphism group, invariant subalgebras, ergodicity, modular theory, and abelian subalgebras. We provide with some examples to support the results. |
| title | Group of automorphisms for strongly quasi invariant states |
| topic | Operator Algebras Mathematical Physics 37N20, 81P16 |
| url | https://arxiv.org/abs/2311.01481 |