Resumen
En esta nota enunciaremos alguans propiedades geométricas de los espacios de Banach, entre las cuales podemos señalar espacios uniformemente convexos, espacios uniformemente no cuadrados, espacios localmente uniformemente convexos, espacios estrictamente convexos, etc., y analizaremos el problema cuando tales propiedades se trasladan al espacio cociente.
Citas
Clarkson, J.A. (1936) “Uniformly Convex Spaces”, Trans. A.M.S.40: 396–414.
Day, M.M. (1973) Normed Linear Spaces,3aedici ́on. Springer-Verlag, New York.
Fan, K.; Glicksberg, I. (1955) “Fully convex normed linear spaces”, Proc. Nat. Acad. Scie. USA.41: 947–953.
Fan, K.; Glicksberg, I. (1958) “Some geometric properties of the spheres in a normed linear space”, Duke Math. Jour.25: 553–568.
Giles, J.R.; Sims, B.; Yorke, A.C. (1990) “On the drop and weakdrop properties for a Banach space”, Bull. Aust. Math. Soc.41: 503–507.
Huff, R. (1980) “Banach spaces which are nearly uniformly convex”, Ruck. Mount. Jour. Math.10: 743–749.
Istratescu, V.I. (s.f.) Strict Convexity and Complex Strict Convexity, Theory and Applications. Marcel Decker, New York.
James, R.C. (1964) “Uniformly non-square Banach space”, Ann. Math. 280: 542–550.
Lin, B.-L.; Zhang, W. (1991) “Some geometric properties related to uniform convex of Banach spaces, function spaces”, Lecture Notes in Pure and Appl. Math. 136, Marcel Decker, New York: 281–294.
Lovaglia, A.R. (1955) “Locally uniformly convex Banach spaces”, Trans. A.M.S. 78: 225–238.
Montesinos, V. (1987) “Drop property equals reflexivity”, Studia Math. 86: 93–100.
Montesinos, V.; Torregrosa, J.R. (s.f.) “Sobre espacios de Banach localmente uniformemente rotundos”.
Phelps, R.R. (1960) “Uniqueness of Hanh-Banach extension and unique best approximation”, Trans. A.M.S. 95: 238–255.
Rolewicz, S. (1987) “On drop property”, Studia Math.85: 27–35.
Chau-Xun, N.; Jian-Hua, W. (1988) “On the Lk−UR and L−kR spaces”, Math. Proc. Camb. Phil. Suc. 104: 521–526.