| Texto completo | |
| Autor(es): |
Caceres-Rigo, Alejandra C.
;
Ferenczi, Valentin
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | STUDIA MATHEMATICA; v. N/A, p. 47-pg., 2025-04-06. |
| Resumo | |
We extend the methods used by V. Ferenczi and Ch. Rosendal to obtain the "third dichotomy" in the program of classification of Banach spaces up to subspaces, in order to prove that a Banach space E with an admissible system of blocks (DE, AE) contains an infinite-dimensional subspace with a basis which is either AE-tight or AEminimal. In this setting we obtain, in particular, dichotomies regarding subsequences of a basis, and as a corollary, we show that every normalized basic sequence (en)n has a subsequence which satisfies a tightness property or is spreading. Other dichotomies between notions of minimality and tightness are demonstrated, and the Ferenczi-Godefroy interpretation of tightness in terms of Baire category is extended to this new context. (AU) | |
| Processo FAPESP: | 17/18976-5 - Estudo da complexidade boreliana de certas propriedades de espaços de Banach |
| Beneficiário: | Alejandra Carolina Cáceres Rigo |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |
| Processo FAPESP: | 16/25574-8 - Geometria dos espaços de Banach |
| Beneficiário: | Valentin Raphael Henri Ferenczi |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 22/04745-0 - Envelopes e ultrahomogeneidade em espaços de Banach |
| Beneficiário: | Valentin Raphael Henri Ferenczi |
| Modalidade de apoio: | Bolsas no Exterior - Pesquisa |
| Processo FAPESP: | 23/12916-1 - Geometria de espaços de Banach |
| Beneficiário: | Valentin Raphael Henri Ferenczi |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |