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arXiv · 2512.14006

Fuglede theorem for symmetric spaces of $\tau$-measurable operators

Denis Potapov·Fedor Sukochev·Anna Tomskova·Dmitriy Zanin
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Abstract

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 $\tau$-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.

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Denis Potapov, Fedor Sukochev, Anna Tomskova, Dmitriy Zanin. 2025-12-16. Fuglede theorem for symmetric spaces of $\tau$-measurable operators. https://arxiv.org/abs/2512.14006

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