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Alejandro Marcos

Publications and source records attributed to Alejandro Marcos.

3 recordsLinked to original sources
arXiv2026

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

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.

math.FA↗
arXiv2026

Remarks about symmetry-type conditions of conditional bases of Banach spaces

We investigate the existence of equivalent p-norms, 0< p 1, under which conditional symmetric or spreading bases in quasi-Banach spaces become isometric. For spreading bases (which need not be unconditional or even Schauder bases), we develop new techniques involving the geometry of spreading sequences and their associated spreading models. We prove that any spreading basis is automatically seminormalized, M-bounded, and uniformly spreading, which allows the construction of an isometric renorming via its spreading model. For symmetric bases, we show they are necessarily spreading and uniformly symmetric, enabling a direct application of a renorming lemma for uniformly bounded semigroups of operators. Consequently, any quasi-Banach space with a symmetric basis admits a renorming making all permutations isometries, and any spreading basis admits a renorming making all increasing maps isometries. These results extend and unify classical isometric renorming theorems for unconditional, subsymmetric, and symmetric Schauder bases to the conditional, non-Schauder setting.

math.FA↗