Embedding unconditional stable banach spaces into symmetric stable banach spaces

Springer Science and Business Media LLC - Tập 53 - Trang 373-380 - 1986
Jesús Bastero1
1Facultad de Ciencias, Universidad de Zaragoza, Zaragoza (Spain)

Tóm tắt

In this paper we prove the following result which solves a question raised by A. Pelczynski: “Every stable Banach space with an unconditional basis is isomorphic to a complemented subspace of some stable Banach space with a symmetric basis.” Moreover, we show that all the interpolation spacesl p ,l q θ,X,1 1≦p, q<∞ andX stable, are stable.

Tài liệu tham khảo

J. Bastero and J. M. Mira,Stabilité des espaces de Banach de suites vectorielles, C.R. Acad. Sci. Paris299 (1984), 339–341. M. A. Canela,Stable quotients of l p, Arch. Math.44 (1985), 446–450. W. Davis,Embedding spaces with unconditional bases, Israel J. Math.20 (1975), 189–191. D. Garling,Stable Banach spaces, random measures and Orlicz function spaces, Springer Lecture Notes928, 1982, pp. 121–175. J. Krivine and B. Maurey,Espaces de Banach stables, Israel J. Math.39 (1981), 273–295. J. Lindenstrauss,A remark on symmetric bases, Israel J. Math.13 (1972), 317–320. J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces I, Springer-Verlag, Berlin, 1977. Y. Raynaud,Sur la propriété de stabilité pour les espaces de Banach, Theses 3eme cicle, Paris VII, 1981. Y. Raynaud,Deux nouveaux exemples d’espaces de Banach stables, C.R. Acad. Sci. Paris292 (1981), 715–717. Y. Raynaud,Stabilité des quotients d’un espace réflexif sous un hypothèse de compacité, preprint. A. Szankowski,Embedding Banach spaces with unconditional basis into spaces with symmetric basis, Israel J. Math.15 (1973), 53–59.