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The UMD property of symmetric operator spaces
Abstract
We prove that if E is a UMD symmetric Banach function space on (0,∞), then E(ℳ,τ) is UMD for every semifinite von Neumann algebra 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.
Related
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BibTeX
@misc{huang2026property,
title = {{The UMD property of symmetric operator spaces}},
author = {J Huang and F Sukochev},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14282},
eprint = {2609.14282},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05748054v1},
}
RIS
TY - UNPB
TI - The UMD property of symmetric operator spaces
AU - J Huang
AU - F Sukochev
PY - 2026
DA - 2026/09/13
PB - HAL
DO - 10.48550/arxiv.2609.14282
UR - https://hal.science/hal-05748054v1
AB - We prove that if E is a UMD symmetric Banach function space on (0,∞), then E(ℳ,τ) is UMD for every semifinite von Neumann algebra 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.
ER -