Geodesic
Un Théorème de Transfert Pour la Propriété des Boules
Canadian mathematical bulletin, Tome 30 (1987) no. 3, pp. 295-300

Voir la notice de l'article provenant de la source Cambridge University Press

We show that, if X and Y are Banach spaces such that X has the Mazur's intersection property and such that there exists T, an operator from Y into X so that T * and T ** are injective, then there exists on Y an equivalent norm which has the Mazur's intersection property.We deduce from this result and from a result of M. Talagrand that there exists on the long James space J(η) an equivalent norm which has the Mazur's intersection property.
DOI : 10.4153/CMB-1987-042-4
Mots-clés : 46B20 
Deville, Robert. Un Théorème de Transfert Pour la Propriété des Boules. Canadian mathematical bulletin, Tome 30 (1987) no. 3, pp. 295-300. doi: 10.4153/CMB-1987-042-4
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[1] 1. Diestel, J., Geometry of Banach spaces, Lecture notes in Maths. N° 485. Google Scholar

[2] 2. Edgar, G.A., Measurability in a Banach space I, Indiana Univ. Math. J. 26 (1977), pp. 663—680. Google Scholar

[3] 3. Edgar, G.A., A long James space, Measure theory , Oberwolfach 1979, Lecture notes in Math. N° 794. Google Scholar

[4] 4. Giles, J.R., Gregory, D.A. and Sims, B., Characterisation of normed linear spaces with M azur's intersection property, Bull. Austral. Math. Soc. 18 (1978), pp. 105–123. Google Scholar

[5] 5. Godefroy, G., Troyanski, S., Whitfield, J. and Zizler, V., Smoothness in Weakly Compactly Generated Banach spaces, J.F.A. 52 (1983), pp. 344–352. Google Scholar

[6] 6. Godefroy, G., Troyansky, S., Whitfield, J. and Zizler, V., Locally uniformly rotund renorming and injections into c(Γ), Canad. Math. Bull. 27(4) (1984), pp. 494–500. Google Scholar

[7] 7. Godefroy, G., Troyansky, S., Whitfield, J. and Zizler, V., Three spaces problem for locally uniformly rotund renorming, A paraître dans Proc. A.M.S. Google Scholar

[8] 8. Dashiell, F.K. and Lindenstrauss, J., Some examples concerning strictly convex norms on (K) spaces, Israel J. of Math. 16(3) (1973), pp. 329–342. Google Scholar

[9] 9. Mazur, S., Uber schwach Kanvergenz in den Raümen (Lp), Studia Math. 4 (1983), pp. 128–133. Google Scholar

[10] 10. Phelps, R.R., A representation theorem for bounded convex sets, Proc. A.M.S. II (1960), pp. 976–983. Google Scholar

[11] 11. Stegall, C., The duality between Asplund spaces and spaces with the Radon-Nikodym property, Israel J. of Math. 29(4) (1978), pp. 408–412. Google Scholar

[12] 12. Talagrand, M., Renormages de quelques (K), Israel J. Math. 54(3) (1986), pp. 327–334. Google Scholar

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