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PreprintCC BY-NC-SA 4.0arXiv

Super McDuff and Uniformly Super McDuff II1 factor

  • Xinyan Cao
  • Zhaolin Yao
  • Xiaoyan Zhou
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Abstract

In this paper, we prove that every super McDuff II1 factor is uniformly super McDuff. In particular, the classes of super McDuff and uniformly super McDuff II1 factors coincide. This answers \cite[Question D]{GJKEP} affirmatively. For factors with separable predual, super McDuffness is therefore equivalent to the Brown property and is preserved under elementary equivalence, also answering \cite[Question~6.2.1]{AGK22} affirmatively. We further show that every infinite tensor product of non-Γ II1 factors is uniformly super McDuff. For a finite tensor product of separable II1 factors that is super McDuff, each tensor factor is either non-Γ or uniformly super McDuff, and at least one is uniformly super McDuff.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026super,
  title = {{Super McDuff and Uniformly Super McDuff $\rm II_1$ factor}},
  author = {Xinyan Cao and Zhaolin Yao and Xiaoyan Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04842},
  eprint = {2611.04842},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04842},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Super McDuff and Uniformly Super McDuff II_1 factor
AU  - Xinyan Cao
AU  - Zhaolin Yao
AU  - Xiaoyan Zhou
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04842
UR  - https://arxiv.org/abs/2611.04842
AB  - In this paper, we prove that every super McDuff II_1 factor is uniformly super McDuff. In particular, the classes of super McDuff and uniformly super McDuff II_1 factors coincide. This answers \cite[Question D]{GJKEP} affirmatively. For factors with separable predual, super McDuffness is therefore equivalent to the Brown property and is preserved under elementary equivalence, also answering \cite[Question~6.2.1]{AGK22} affirmatively. We further show that every infinite tensor product of non-Γ II_1 factors is uniformly super McDuff. For a finite tensor product of separable II_1 factors that is super McDuff, each tensor factor is either non-Γ or uniformly super McDuff, and at least one is uniformly super McDuff.
ER  -