Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-05T04:04:30.652Z Has data issue: false hasContentIssue false

Homéomorphismes Uniformes Entre les Sphères Unité des Espaces D'Interpolation

Published online by Cambridge University Press:  20 November 2018

Mohamad Daher*
Affiliation:
Université Paris VII, Paris, France
Rights & Permissions [Opens in a new window]

Résumé

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Si (A0,A1) est un couple d'interpolation et si A0 est uniformément convexe on montre que pour tous θ1, θ2 ∊ ]0,1 [ il existe un homéomorphisme uniforme entre la sphère unité de (A0,A1)θ1 et la sphère unité de (A0, A1)θ2.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Beauzamy, B., Introduction to Banach spaces and their geometry, Notas Mat., North-Holland.Google Scholar
2. Bergh, J. and Löfström, J., Interpolation spaces, Springer-Verlag 223,Berlin, Heidelberg, New York, 1976.Google Scholar
3. Bergh, J., On the relation between the two complex methods of interpolation, Indiana Univ. Math. J. 28 (1979), 775777.Google Scholar
4. Calderon, A. P., Intermediate spaces and interpolation the complex method, Studia Math. 24(1964), 113—190.Google Scholar
5. Chaatit, F., On uniform homeomorphisms of the unit spheres of certain Banach Lattices, à paraître.Google Scholar
6. Cwikel, M., Complex interpolation spaces, a discrete definition and reiteration, Indiana Univ. Math. J., (1978), 1005-1009.Google Scholar
7. Cwikel, M. and Reisner, S., Interpolation of uniformly convex Banach spaces, Proc. Amer. Math. Soc. 84(1982), 555559.Google Scholar
8. Diestel, J. and Uhl, J. J., Vector measures, Math. Surveys 15, Amer. Math. Soc., 1977.Google Scholar
9. Enflo, P., On a problem ofSmirnov, Ark. Mat. 8(1969), 107109.Google Scholar
10. Figiel, T. et Pisier, G., Séries aléatoires dans les espaces uniformément convexes ou uniformément lisses, C. R. Acad. Sci. Paris (A) 279(1974), 611—614.Google Scholar
11. Haagerup, U. and Pisier, G., Factorization of analytic functions with values in non-commutative L\-spaces and applications, Canad. J. Math. XLI(1989), 882906.Google Scholar
12. Kalton, N. J., communication personnelle. Google Scholar
13. Lindenstrauss, J. etTzafriri, L., Classical Banach spaces, Vol.2, Ergeb. Math. Grenzgeb. 97, Springer Verlag, 1979.Google Scholar
14. Maurey, B. et Pisier, G., Séries de variables aléatoires indépendantes et propriétés géométriques des espaces de Banach, Studia Math. 58(1976), 4590.Google Scholar
15. Odell, E. et Th. Schlumprecht, The distortion problem, Acta Math., (1995).Google Scholar
16. Pisier, G., Some applications of the complex interpolation method to Banach Lattices, J. Anal. Math. 35(1979), 264281.Google Scholar