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The role of symmetry in the performance of the Thresholding Greedy Algorithm

  • José L. Ansorena
  • Miguel Berasategui
  • Alejandro Marcos
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Abstract

This paper continues the study of conditional symmetric systems initiated in arXiv:2601.15784 and solves several problems posed there. While the interaction between unconditionality and symmetry is well known in the Banach setting following the work in arXiv:2304.05888 and arXiv:2601.15784, we broaden the scope and address similar questions for spreading systems in the more general setting of quasi-Banach spaces. Our aim is twofold. On the one hand, we characterize which spreading systems of Banach spaces are unconditional. On the other hand, we provide examples of quasi-Banach spaces equipped with conditional systems with symmetry-related properties to illustrate the connections between symmetry, greedy-like properties, and the Schauder basis property in the absence of local convexity.

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Cite

BibTeXRIS
BibTeX
@misc{ansorena2026role,
  title = {{The role of symmetry in the performance of the Thresholding Greedy Algorithm}},
  author = {José L. Ansorena and Miguel Berasategui and Alejandro Marcos},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41568},
  eprint = {2610.41568},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41568},
}
RIS
TY  - UNPB
TI  - The role of symmetry in the performance of the Thresholding Greedy Algorithm
AU  - José L. Ansorena
AU  - Miguel Berasategui
AU  - Alejandro Marcos
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41568
UR  - https://arxiv.org/abs/2610.41568
AB  - This paper continues the study of conditional symmetric systems initiated in arXiv:2601.15784 and solves several problems posed there. While the interaction between unconditionality and symmetry is well known in the Banach setting following the work in arXiv:2304.05888 and arXiv:2601.15784, we broaden the scope and address similar questions for spreading systems in the more general setting of quasi-Banach spaces. Our aim is twofold. On the one hand, we characterize which spreading systems of Banach spaces are unconditional. On the other hand, we provide examples of quasi-Banach spaces equipped with conditional systems with symmetry-related properties to illustrate the connections between symmetry, greedy-like properties, and the Schauder basis property in the absence of local convexity.
ER  -