| Texto completo | |
| Autor(es): |
Rincon-Villamizar, Michael A.
;
Uzcategui-Aylwin, Carlos
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Mathematical Analysis and Applications; v. 536, n. 2, p. 19-pg., 2024-03-13. |
| Resumo | |
We study the space c (0,I )( X ) of all bounded sequences (x(n)) in a Banach space X that I - converges to 0 , endowed with the sup norm, where I is an ideal of subsets of N. Our results contribute to the development of a structural theory for these spaces. We show that two such spaces, c(0,I) and c(0, J), are isometric exactly when the ideals I and J are isomorphic. Additionally, we analyze the connection of the well-known Kat & ecaron;tov pre-order <= K on ideals with some properties of the space c( 0, I ). For instance, we show that I <= K J exactly when there is a (not necessarily onto) Banach lattice isometry from c(0,I) to c(0,J), satisfying some additional conditions. We present some lattice-theoretic properties of c(0, I ), particularly demonstrating that every closed ideal of l(infinity) is equal to c(0,I) for some ideal I on N. We also show that certain classical Banach spaces are isometric to c 0, I for some ideal I, such as the spaces l(infinity) (c(0)) and c(0) (l (infinity)). Finally, we provide several examples of ideals for which c(0, I) is not a Grothendieck space. (AU) | |
| Processo FAPESP: | 21/01144-2 - Ideais associados a sequências em espaços de Banach e derivações Lipschitz em espaços de Hilbert |
| Beneficiário: | Michael Alexánder Rincón Villamizar |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |