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INICIO |
27 de julio de 2024
Weak sequential completeness of sequence spaces.
| Título inglés | Weak sequential completeness of sequence spaces. |
|---|---|
| Título español | Completitud secuencial débil de espacios de sucesiones. |
| Autor/es | Swartz, Charles |
| Organización | Dep. Math. Sci. New Mexico State Univ., Las Cruces (New Mexico), Estados Unidos |
| Revista | 0010-0757 |
| Publicación | 1992, 43(1): 55-61, 9 Ref. |
| Tipo de documento | articulo |
| Idioma | Inglés |
| Resumen inglés | Köthe and Toeplitz introduced the theory of sequence spaces and established many of the basic properties of sequence spaces by using methods of classical analysis. Later many of these same properties of sequence spaces were reestablished by using soft proofs of functional analysis. In this note we would like to point out that an improved version of a classical lemma of Schur due to Hahn can be used to give very short proofs of two of the weak sequential completeness results of Köthe and Toeplitz. One of our proofs actually gives an improvement of one of the completeness results of Köthe and Toeplitz which was obtained by Benett using functional analysis methods and the method of proof is used in paragraph 3 to obtain a completeness result for ß-duals of vector-valued sequence spaces. One of our completeness results is employed to obtain a more general form of a Hellinger-Toeplitz type theorem for sequence spaces due to Köthe and the second completeness result is employed to obtain another Hellinger-Toeplitz type theorem for sequence spaces which covers additional cases not covered by Köthe's result. |
| Clasificación UNESCO | 120222 |
| Palabras clave español | Completitud ; Espacios de Banach ; Análisis secuencial ; Espacios vectoriales topológicos |
| Código MathReviews | MR1214223 |
| Código Z-Math | Zbl 0782.46013 |
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