Geodesic
Topological Properties of the Set of Norm-Attaining Linear Functionals
Canadian journal of mathematics, Tome 47 (1995) no. 2, pp. 318-329

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

If X is a separable non-reflexive Banach space, then the set NA of all norm-attaining elements of X * is not a w *-G δ subset of X *. However if the norm of X is locally uniformly rotund, then the set of norm attaining elements of norm one is w *-G δ. There exist separable spaces such that NA is a norm-Borel set of arbitrarily high class. If X is separable and non-reflexive, there exists an equivalent Gâteaux-smooth norm on X such that the set of all Gâteaux-derivatives is not norm-Borel.
DOI : 10.4153/CJM-1995-017-3
Mots-clés : 46B20, 04A15 
Debs, Gabriel; Godefroy, Gilles; Raymond, Jean Saint. Topological Properties of the Set of Norm-Attaining Linear Functionals. Canadian journal of mathematics, Tome 47 (1995) no. 2, pp. 318-329. doi: 10.4153/CJM-1995-017-3
@article{10_4153_CJM_1995_017_3,
     author = {Debs, Gabriel and Godefroy, Gilles and Raymond, Jean Saint},
     title = {Topological {Properties} of the {Set} of {Norm-Attaining} {Linear} {Functionals}},
     journal = {Canadian journal of mathematics},
     pages = {318--329},
     year = {1995},
     volume = {47},
     number = {2},
     doi = {10.4153/CJM-1995-017-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-017-3/}
}
TY  - JOUR
AU  - Debs, Gabriel
AU  - Godefroy, Gilles
AU  - Raymond, Jean Saint
TI  - Topological Properties of the Set of Norm-Attaining Linear Functionals
JO  - Canadian journal of mathematics
PY  - 1995
SP  - 318
EP  - 329
VL  - 47
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-017-3/
DO  - 10.4153/CJM-1995-017-3
ID  - 10_4153_CJM_1995_017_3
ER  - 
%0 Journal Article
%A Debs, Gabriel
%A Godefroy, Gilles
%A Raymond, Jean Saint
%T Topological Properties of the Set of Norm-Attaining Linear Functionals
%J Canadian journal of mathematics
%D 1995
%P 318-329
%V 47
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-017-3/
%R 10.4153/CJM-1995-017-3
%F 10_4153_CJM_1995_017_3

[1] 1. Bishop, E. and Phelps, R.R., A proof that every Banach space is suhreflexive, Bull. Amer. Math. Soc. 67(1961), 97–98. Google Scholar

[2] 2. Deville, R., Godefroy, G. and Zizler, V., Smoothness and Renormings in Banach spaces, Pitman Monographs and Surveys Pure Appl. Math. 64, Longman Ed., 1993. Google Scholar

[3] 3. Fabian, M., Preiss, D., Whitfield, J.H.M. and Zizler, V., Separating polynomials on Banach spaces, Quart. J. Math. Oxford Ser. (2) 40(1989), 40SM22. Google Scholar

[4] 4. James, R.C., Weakly compact sets, Trans. Amer. Math. Soc. 113(1964), 129–140. Google Scholar

[5] 5. Kaufman, R., Topics on analytic sets, Fund. Math. 139(1991), 215–220. Google Scholar

[6] 6. Moschovakis, Y., Descriptive set theory, North Holland, Amsterdam, 1980. Google Scholar

[7] 7. Partington, J.R., Equivalent norms on spaces of hounded functions, Israel J. Math. 35(1980), 205–209. Google Scholar

[8] 8. Preiss, D. and Zajicek, L., Fréchet differentiation of convex functions in Banach space with separable dual, Proc. Amer. Math. Soc. 91(1984), 202–204. Google Scholar

[9] 9. Pryce, J.D., Weak compactness in locally convex spaces, Proc. Amer. Math. Soc. 17(1966), 148–155. Google Scholar

[10] 10. Saint Raymond, J., Convergence d'une suite de fonctions, Bull. Sci. Math. 96(1972), 145–150. Google Scholar

[11] 11. Simons, S., A convergence theorem with boundary, Pacific J. Math. 40(1972), 703–708. Google Scholar

[12] 12. Troyanski, S., On a property of the norm which is close to local uniform convexity, Math. Ann. 271(1985), 305–313. Google Scholar

[13] 13. Wadge, W.W., Ph.D. thesis, Berkeley, 1984. Google Scholar

Cité par Sources :