On a theorem by Lions and Peetre about interpolation between a banach space and its dual

Houston Journal of Mathematics

Volumn 24, Issue 2, 1998, Pages 325-344

  Cobos, Fernando ^a   Schonbek, Tomas ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032441024     PISSN: 03621588     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. W.O. Amrein and A. Boutet de Monvel and V. Georgescu, Co-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians, Birkhäuser Verlag, Progress in Mathematics, 135, 1996, Basel.
2. B. Beauzamy, Espaces d'Interpolation Réels: Topologie et Géométrie, Springer Verlag, Lecture Notes, 666, 1978, Heidelberg/New York.
3. J. Bergh, On the relation between the two methods of interpolation, Indiana Univ. Math. J., 28, 1979, 775-778.
4. J. Bergh and J. Löfström, Interpolation Spaces Springer Verlag, 1976, Heidelberg/New York.
5. A. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math., 24 (1964), pp. 113-190.
6. F. Cobos and T. Kühn and J. Peetre, Schatten-Von-Neumann classes of multilinear forms, Duke Math. J., 65 (1992), pp. 121-156.
7. M. Cwikel, Monotonicity properties of interpolation spaces, Arkiv Mat., 14 (1976), pp. 213-236.
8. M. Cwikel and A. Sharif, Complex interpolation spaces generated by the Gagliardo completion of an arbitrary Banach couple, Israel Mathematics Conference Proceedings, 5, Bar Ilan University, Amer. Math. Soc., Providence, RI, 1992, pp. 57-59.
9. I.C. Gohberg and M.G. Kreǐn, Introduction to the Theory of Linear Nonselfadjoint Operators, American Mathematical Soc., Translations of Mathematical Monographs, 18, 1969, Providence, RI.
10. 1 -spaces and applications, Canadian J. Math., 41, 1989, pp. 882-906.
11. S. Janson and P. Nilsson and J. Peetre and M. Zafran, Notes on Wolff's note on interpolation spaces, Proc. London Math. Soc., 48 (1984), pp. 283-299.
12. H. König, On the Fourier coefficients of vector-valued functions, Math. Nachr., 152 (1991), pp. 215-227.
13. J.L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math., 19 (1964), pp. 5-68.
14. L. Maligranda, Interpolation between sum and intersection of Banach spaces, J. Approximation Theory, 47 (1986), pp. 42-53.
15. K. Miyazaki, Some remarks on intermediate spaces, Bull. Kyushu Inst. Tech., 15 (1968), pp. 1-23.
16. J. Peetre, Sur la transformation de Fourier des fonctions a valeurs vectorielles, Rend. Sem. Mat. Univ. Padova, 42 (1969), pp. 15-26.
17. J. Peetre, Paracommutators and minimal spaces, Operators and Function Theory, Proceedings of the NATO Advanced Study Institute on Operators and Function Theory, Lancaster, 1984, ed. S. C. Power, Reidel, Dordrecht, 1985, pp. 163-223.
18. G. Pisier, The operator Hubert space OH, complex interpolation and tensor norms, Memoirs Amer. Math. Soc., 122 no. 585, 1996.
19. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North Holland, 1978, Amsterdam.
20. F. Watbled, Interpolation complexe d'un espace de Banach et de son dual, C.R. Acad. Sci. Paris, Sèrie I, 321 (1995), pp. 1437-1440.
21. F. Watbled, Ensembles de Rosenthal pour des fonctions à valeurs dans un espace de Banach. Interpolation complexe d'un espace de Banach et de son dual, Thèse, Univ. Paris 7, 1996.
22. Q. Xu, Interpolation of operator spaces, J. Funct. Analysis, 139 (1996) pp. 500-539.