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PreprintarXiv licencearXiv

Characterizations of the unit vector basis of c0 or ℓp among minimal systems

  • Miguel Berasategui
  • Pablo M. Berná
  • Stephen J. Dilworth
  • Denka Kutzarova
  • Timur Oikhberg
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Abstract

Given a minimal system E for a Banach space X, Casazza, Dilworth, Kutzarova and Motakis introduced a multiplication ⊗ on span(E) and studied the Schauder bases for which |x ⊗ y|≈ |x||y| asking whether every such basis is equivalent to the canonical unit vector basis of c0 or ℓp. We continue this study in the more general setting of minimal systems that are not assumed to be Schauder bases, and we obtain positive answers under hypotheses that are formally weaker than the ones considered so far: partial democracy instead of democracy or bidemocracy, and truncation quasi-greediness instead of quasi-greediness. Along the way we show that the above multiplicative estimate forces invariance under translations, we characterize when such a minimal system is a Schauder basis, and we give examples showing that the one-sided variants of the estimate behave very differently.

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Cite

BibTeXRIS
BibTeX
@misc{berasategui2026characterizations,
  title = {{Characterizations of the unit vector basis of $c_0$ or $\ell_p$ among minimal systems}},
  author = {Miguel Berasategui and Pablo M. Berná and Stephen J. Dilworth and Denka Kutzarova and Timur Oikhberg},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35726},
  eprint = {2610.35726},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35726},
}
RIS
TY  - UNPB
TI  - Characterizations of the unit vector basis of c_0 or ℓ_p among minimal systems
AU  - Miguel Berasategui
AU  - Pablo M. Berná
AU  - Stephen J. Dilworth
AU  - Denka Kutzarova
AU  - Timur Oikhberg
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35726
UR  - https://arxiv.org/abs/2610.35726
AB  - Given a minimal system E for a Banach space X, Casazza, Dilworth, Kutzarova and Motakis introduced a multiplication ⊗ on span(E) and studied the Schauder bases for which |x ⊗ y|≈ |x||y| asking whether every such basis is equivalent to the canonical unit vector basis of c_0 or ℓ_p. We continue this study in the more general setting of minimal systems that are not assumed to be Schauder bases, and we obtain positive answers under hypotheses that are formally weaker than the ones considered so far: partial democracy instead of democracy or bidemocracy, and truncation quasi-greediness instead of quasi-greediness. Along the way we show that the above multiplicative estimate forces invariance under translations, we characterize when such a minimal system is a Schauder basis, and we give examples showing that the one-sided variants of the estimate behave very differently.
ER  -