Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 18 min ago
PreprintCC BY-NC-ND 4.0arXiv

On complemented subspaces of L1[0,1]

  • Antonio Acuaviva
Open at sourcePDFDOICite

Abstract

We construct two complemented subspaces of L1[0,1]. The first has the Schur property but fails the Radon--Nikodým property. The second contains a copy of ℓ2 but no copy of L1[0,1]. Neither space is isomorphic to a Banach lattice. This gives a negative answer to the complemented-subspace question of Lindenstrauss and Rosenthal. A Lean 4 formalisation of the main results accompanies the paper.

Related

  1. A negative solution to the complemented subspace problem for Banach spaces with unconditional bases
    Antonio Acuaviva
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsarXiv
  2. Subspaces of L1 spanned by the even and odd levels of the Haar system
    Thomas Speckhofer
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Affine Coordinate Subspaces and Strong Khintchine Convergence
    Zirui Jiang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Completely symmetric subspaces of noncommutative Lp-spaces
    Jinghao Huang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Acceleration of the Method of Alternating Projections on subspaces by GMRES
    Luis Manuel Hernández-Ramos, Maryam Calles-Cabriles, Gorka Emaldi-Porco
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@misc{acuaviva2026complemented,
  title = {{On complemented subspaces of $L_1[0,1]$}},
  author = {Antonio Acuaviva},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17283},
  eprint = {2609.17283},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17283},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On complemented subspaces of L_1[0,1]
AU  - Antonio Acuaviva
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17283
UR  - https://arxiv.org/abs/2609.17283
AB  - We construct two complemented subspaces of L_1[0,1]. The first has the Schur property but fails the Radon--Nikodým property. The second contains a copy of ℓ_2 but no copy of L_1[0,1]. Neither space is isomorphic to a Banach lattice. This gives a negative answer to the complemented-subspace question of Lindenstrauss and Rosenthal. A Lean 4 formalisation of the main results accompanies the paper.
ER  -