Presentación | Participantes | Bibliografía (DML-E) | Bibliografía adicional | Enlaces de interés | Otros proyectos DML | Ayuda
INICIO |
27 de julio de 2024
Supertauberian operators and perturbations.
| Título inglés | Supertauberian operators and perturbations. |
|---|---|
| Título español | Operadores supertauberianos y perturbaciones. |
| Autor/es | González, M. ; Martínez-Abejón, A. |
| Organización | Fac. Cienc. Secc. Mat. Univ. Cantabria, Santander, España;Dep. Mat. Fac. Biol. Univ. Oviedo, Oviedo, España |
| Revista | 0213-8743 |
| Publicación | 1993, 8 (2-3): 92-97, 8 Ref. |
| Tipo de documento | articulo |
| Idioma | Inglés |
| Resumen inglés | Upper semi-Fredholm operators and tauberian operators in Banach spaces admit the following perturbative characterizations [6], [2]: An operator T: X --> Y is upper semi-Fredholm (tauberian) if and only if for every compact operator K: X --> Y the kernel N(T+K) is finite dimensional (reflexive). In [7] Tacon introduces an intermediate class between upper semi-Fredholm operators and tauberian operators, the supertauberian operators, and he studies this class using non-standard analysis. Here we study supertauberian operators using ultrapower of Banach spaces and, among other results, we obtain a perturbative characterization. As a consequence we characterize Banach spaces in which all superreflexive subspaces are finite dimensional, and Banach spaces in which all reflexive subspaces are superreflexive. Similar results are obtained for the dual class of cosupertauberian operators, including a perturbative characterization of this class, and characterizations of Banach spaces in which all quotients are finite dimensional, and Banach spaces in which all reflexive quotients are superreflexive. |
| Clasificación UNESCO | 120203 |
| Palabras clave español | Algebra de operadores ; Espacios de Banach ; Espacio reflexivo ; Operadores de Fredholm ; Teoría de perturbación |
| Código MathReviews | MR1285731 |
| Código Z-Math | Zbl 1034.47501 |
 Acceso al artículo completo |
|