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PreprintarXiv licencearXiv

Kalton-Peck space is not isomorphic to its hyperplanes

  • A. Das
  • V. Ferenczi
  • Ch. Rosendal
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Abstract

Let Z2 denote the real Kalton-Peck space. No hyperplane of Z2 admits a complex structure, and Z2 is even in the sense of Ferenczi-Galego. Therefore, Z2 is not linearly isomorphic to its hyperplanes, solving a long-standing conjecture in Banach space theory. The argument uses the Kalton-Swanson symplectic form on Z2, the Castillo-González-Pino Fredholm theorem in Z2, and a special case of a mod-$2$ theorem of Li-Zhu on skew-adjoint Fredholm relations in symplectic spaces, for which a self-contained proof is included.

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Cite

BibTeXRIS
BibTeX
@misc{das2026kaltonpeck,
  title = {{Kalton-Peck space is not isomorphic to its hyperplanes}},
  author = {A. Das and V. Ferenczi and Ch. Rosendal},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.02126},
  eprint = {2608.02126},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.02126},
}
RIS
TY  - UNPB
TI  - Kalton-Peck space is not isomorphic to its hyperplanes
AU  - A. Das
AU  - V. Ferenczi
AU  - Ch. Rosendal
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2608.02126
UR  - https://arxiv.org/abs/2608.02126
AB  - Let Z_2 denote the real Kalton-Peck space. No hyperplane of Z_2 admits a complex structure, and Z_2 is even in the sense of Ferenczi-Galego. Therefore, Z_2 is not linearly isomorphic to its hyperplanes, solving a long-standing conjecture in Banach space theory. The argument uses the Kalton-Swanson symplectic form on Z_2, the Castillo-González-Pino Fredholm theorem in Z_2, and a special case of a mod-$2$ theorem of Li-Zhu on skew-adjoint Fredholm relations in symplectic spaces, for which a self-contained proof is included.
ER  -