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arXiv · 2609.14282

The UMD property of symmetric operator spaces

Jinghao Huang·Fedor Sukochev
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Abstract

We prove that if $E$ is a UMD symmetric Banach function space on $(0,\infty)$, then $E(\mathcal{M},τ)$ is UMD for every semifinite von Neumann algebra $\mathcal{M}$ equipped with a faithful normal semifinite trace $τ$. This resolves in the affirmative an open problem that has circulated in the non-commutative world for more than four decades.

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Jinghao Huang, Fedor Sukochev. 2026-09-13. The UMD property of symmetric operator spaces. https://arxiv.org/abs/2609.14282

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