Continuity of the uniform rotundity modulus relative to linear subspaces
Fernández, Manuel ; Palacios, Isidro
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 273-277 / Harvested from Czech Digital Mathematics Library

We prove the continuity of the rotundity modulus relative to linear subspaces of normed spaces. As a consequence we reduce the study of uniform rotundity relative to linear subspaces to the study of the same property relative to closed linear subspaces of Banach spaces.

Publié le : 1997-01-01
Classification:  46B20
@article{118925,
     author = {Manuel Fern\'andez and Isidro Palacios},
     title = {Continuity of the uniform rotundity modulus relative to linear subspaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {273-277},
     zbl = {0886.46013},
     mrnumber = {1455494},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118925}
}
Fernández, Manuel; Palacios, Isidro. Continuity of the uniform rotundity modulus relative to linear subspaces. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 273-277. http://gdmltest.u-ga.fr/item/118925/

Clarkson J.A. Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396-414. (1936) | MR 1501880 | Zbl 0015.35604

Fakhoury H. Directions d'uniform convexité dans un space normé, Séminaire Choquet, 14 anné, No. 6 (1974).

Fernández M.; Palacios I. Relative rotundity in $L^p(X)$, Arch. Math. (Basel) 65 (1995), 61-68. (1995) | MR 1336225

Fernández M.; Palacios I. Directional uniform rotundity in spaces of essentially bounded vector functions, to appear in Proc. Amer. Math. Soc. | MR 1350942

Garkavi A.L. The best possible net and the best possible cross-section of a set in a normed space, Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 87-106 Amer. Math. Soc. Transl. Ser. 2 39 (1964), 111-132. (1964) | MR 0136969

Goebel K.; Kirk W.A. Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics No. 28, Cambridge Univ. Press, Cambridge, MA, 1990. | MR 1074005

Kamińska A.; Turett B. Some remarks on moduli of rotundity in Banach spaces, Acad. Scien. Math. Vol. 36, No. 5-6, 1988. | MR 1101665

Lindenstrauss J.; Tzafriri L. Classical Banach Space II, Springer-Verlag, Berlin-Heidelberg-New York, 1979. | MR 0540367

Ullán A. Módulos de Convexidad y Lisura en Espacios Normados, Publ. Dep. Matemáticas Univ. Extremadura, No. 27, Badajoz, 1991. | MR 1174971