The similarity of irreducible operators in factors
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911632011034624 |
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| author | Ma, Minghui Shi, Rui Yang, Shanshan |
| author_facet | Ma, Minghui Shi, Rui Yang, Shanshan |
| contents | An operator $T$ in a separable factor $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann subalgebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e., $W^*(T)'\cap\mathcal{M}=\mathbb{C}I$. We say that $T$ is a single generator of $\mathcal{M}$ if $W^*(T)=\mathcal{M}$. In this paper, we study generators of separable factors related to maximal abelian self-adjoint subalgebras. As an application, we obtain a complete characterization of normal operators in separable factors which are similar to irreducible operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21482 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The similarity of irreducible operators in factors Ma, Minghui Shi, Rui Yang, Shanshan Operator Algebras Functional Analysis 47C15, 46L10 An operator $T$ in a separable factor $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann subalgebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e., $W^*(T)'\cap\mathcal{M}=\mathbb{C}I$. We say that $T$ is a single generator of $\mathcal{M}$ if $W^*(T)=\mathcal{M}$. In this paper, we study generators of separable factors related to maximal abelian self-adjoint subalgebras. As an application, we obtain a complete characterization of normal operators in separable factors which are similar to irreducible operators. |
| title | The similarity of irreducible operators in factors |
| topic | Operator Algebras Functional Analysis 47C15, 46L10 |
| url | https://arxiv.org/abs/2604.21482 |