Fuglede theorem for symmetric spaces of $τ$-measurable operators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908714467852288 |
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| author | Potapov, Denis Sukochev, Fedor Tomskova, Anna Zanin, Dmitriy |
| author_facet | Potapov, Denis Sukochev, Fedor Tomskova, Anna Zanin, Dmitriy |
| contents | We extend the classical Fuglede commutativity theorem to the full scale of symmetrically normed operator ideals. Our main result provides a complete characterization: a symmetric ideal or symmetric operator space of $τ$-measurable operators satisfies the Fuglede theorem if and only if its commutative core has non-trivial Boyd indices, or equivalently, if it is an interpolation space in the scale of $L_p$-spaces for $1<p<\infty$. This criterion subsumes all previously known cases, including Lorentz and Schatten classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14006 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fuglede theorem for symmetric spaces of $τ$-measurable operators Potapov, Denis Sukochev, Fedor Tomskova, Anna Zanin, Dmitriy Functional Analysis We extend the classical Fuglede commutativity theorem to the full scale of symmetrically normed operator ideals. Our main result provides a complete characterization: a symmetric ideal or symmetric operator space of $τ$-measurable operators satisfies the Fuglede theorem if and only if its commutative core has non-trivial Boyd indices, or equivalently, if it is an interpolation space in the scale of $L_p$-spaces for $1<p<\infty$. This criterion subsumes all previously known cases, including Lorentz and Schatten classes. |
| title | Fuglede theorem for symmetric spaces of $τ$-measurable operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2512.14006 |