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PreprintCC BY 4.0arXiv

Expansive operators on Fréchet spaces without continuous norm

  • Antoni López-Martínez
  • Quentin Menet
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Abstract

We investigate the existence of (metrically) expansive operators on Fréchet spaces without continuous norm. We first solve a problem posed by Bernardes, Caraballo, Darji, Fávaro, and Peris in 2025, by showing that there is no expansive operator on the Fréchet space ω of all sequences. We prove this fact by investigating the existence of orbits remaining cofinitely inside some fixed closed subspace of finite codimension. We then give examples of expansive operators on some other Fréchet spaces without continuous norm.

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Cite

BibTeXRIS
BibTeX
@misc{lopezmartinez2026expansive,
  title = {{Expansive operators on Fréchet spaces without continuous norm}},
  author = {Antoni López-Martínez and Quentin Menet},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19954},
  eprint = {2610.19954},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19954},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Expansive operators on Fréchet spaces without continuous norm
AU  - Antoni López-Martínez
AU  - Quentin Menet
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19954
UR  - https://arxiv.org/abs/2610.19954
AB  - We investigate the existence of (metrically) expansive operators on Fréchet spaces without continuous norm. We first solve a problem posed by Bernardes, Caraballo, Darji, Fávaro, and Peris in 2025, by showing that there is no expansive operator on the Fréchet space ω of all sequences. We prove this fact by investigating the existence of orbits remaining cofinitely inside some fixed closed subspace of finite codimension. We then give examples of expansive operators on some other Fréchet spaces without continuous norm.
ER  -