The inter-relationship between isomorphisms of commutative and isomorphisms of non-commutative $\log$-algebras
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913478925615104 |
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| author | Abdullaev, Rustam Azizov, Azizkhon |
| author_facet | Abdullaev, Rustam Azizov, Azizkhon |
| contents | This paper establishes a necessary and sufficient condition for the coincidence of non-commutative $\log$-algebras constructed from different exact normal semifinite traces. Consequently, we provide a criterion for the isomorphism of $\log$-algebras built on non-commutative von Neumann algebras with different exact normal semifinite traces. Additionally, we demonstrate a connection between the isomorphism of non-commutative $\log$-algebras and the isomorphism of the corresponding $\log$-algebras constructed on the center of these von Neumann algebras. Furthermore, we present a necessary and sufficient condition for the isomorphism of $\log$-algebras derived from different von Neumann algebras of type $I_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13527 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The inter-relationship between isomorphisms of commutative and isomorphisms of non-commutative $\log$-algebras Abdullaev, Rustam Azizov, Azizkhon Functional Analysis Operator Algebras 46A16, 46B04, 46E30 This paper establishes a necessary and sufficient condition for the coincidence of non-commutative $\log$-algebras constructed from different exact normal semifinite traces. Consequently, we provide a criterion for the isomorphism of $\log$-algebras built on non-commutative von Neumann algebras with different exact normal semifinite traces. Additionally, we demonstrate a connection between the isomorphism of non-commutative $\log$-algebras and the isomorphism of the corresponding $\log$-algebras constructed on the center of these von Neumann algebras. Furthermore, we present a necessary and sufficient condition for the isomorphism of $\log$-algebras derived from different von Neumann algebras of type $I_n$. |
| title | The inter-relationship between isomorphisms of commutative and isomorphisms of non-commutative $\log$-algebras |
| topic | Functional Analysis Operator Algebras 46A16, 46B04, 46E30 |
| url | https://arxiv.org/abs/2408.13527 |