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PreprintCC BY 4.0arXiv

Quotients of L1 by subsequences of the Haar system have cotype 2

  • Stephen Dilworth
  • Denka Kutzarova
  • Mikhail Ostrovskii
  • Thomas Speckhofer
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Abstract

Let Y be the closed linear span of a subsequence of the Haar system in L1. We prove that the quotient space L1/Y has cotype~$2$. This result implies that transportation cost spaces on diamond graphs have cotype $2$.

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Cite

BibTeXRIS
BibTeX
@misc{dilworth2026quotients,
  title = {{Quotients of $L_1$ by subsequences of the Haar system have cotype 2}},
  author = {Stephen Dilworth and Denka Kutzarova and Mikhail Ostrovskii and Thomas Speckhofer},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31542},
  eprint = {2609.31542},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31542},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quotients of L_1 by subsequences of the Haar system have cotype 2
AU  - Stephen Dilworth
AU  - Denka Kutzarova
AU  - Mikhail Ostrovskii
AU  - Thomas Speckhofer
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31542
UR  - https://arxiv.org/abs/2609.31542
AB  - Let Y be the closed linear span of a subsequence of the Haar system in L_1. We prove that the quotient space L_1/Y has cotype~$2$. This result implies that transportation cost spaces on diamond graphs have cotype $2$.
ER  -