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The $2$-co-lacunary subsequence principle for arbitrary noncommutative L1-spaces

  • Jinghao Huang
  • Yunpeng Zhu
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Abstract

For every von Neumann algebra M, we prove that each bounded sequence in the Haagerup space L1(M)=M* admits either a norm-convergent subsequence or a 2-co-lacunary subsequence. This answers an open problem of Parcet and Randrianantoanina \cite[Remark~3.11]{ParcetRandrianantoanina2006} and removes both hyperfiniteness and semifiniteness.

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Cite

BibTeXRIS
BibTeX
@misc{huang20262colacunary,
  title = {{The $2$-co-lacunary subsequence principle for arbitrary noncommutative $L_1$-spaces}},
  author = {Jinghao Huang and Yunpeng Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18008},
  eprint = {2610.18008},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18008},
}
RIS
TY  - UNPB
TI  - The $2$-co-lacunary subsequence principle for arbitrary noncommutative L_1-spaces
AU  - Jinghao Huang
AU  - Yunpeng Zhu
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18008
UR  - https://arxiv.org/abs/2610.18008
AB  - For every von Neumann algebra M, we prove that each bounded sequence in the Haagerup space L_1(M)=M_* admits either a norm-convergent subsequence or a 2-co-lacunary subsequence. This answers an open problem of Parcet and Randrianantoanina \cite[Remark~3.11]{ParcetRandrianantoanina2006} and removes both hyperfiniteness and semifiniteness.
ER  -