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PreprintCC BY 4.0arXiv

The Rademacher quotient of L1 embeds into L1 and its weak Calkin algebra is uniformly incompressible

  • Amir Bahman Nasseri
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Abstract

Let R be the closed linear span of the Rademacher functions in L1(0,1). We prove that L1(0,1)/R embeds isomorphically into L1(0,1), answering affirmatively a question of González and Martínez-Abejón \cite[p.~140]{GM97}. We then use this embedding to show that the weak Calkin algebra of the quotient is uniformly incompressible. \end{abstract

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Cite

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BibTeX
@misc{nasseri2026rademacher,
  title = {{The Rademacher quotient of $L^1$ embeds into $L^1$ and its weak Calkin algebra is uniformly incompressible}},
  author = {Amir Bahman Nasseri},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26984},
  eprint = {2609.26984},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26984},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Rademacher quotient of L^1 embeds into L^1 and its weak Calkin algebra is uniformly incompressible
AU  - Amir Bahman Nasseri
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26984
UR  - https://arxiv.org/abs/2609.26984
AB  - Let R be the closed linear span of the Rademacher functions in L^1(0,1). We prove that L^1(0,1)/R embeds isomorphically into L^1(0,1), answering affirmatively a question of González and Martínez-Abejón \cite[p.~140]{GM97}. We then use this embedding to show that the weak Calkin algebra of the quotient is uniformly incompressible. \end{abstract
ER  -