High order smoothness and asymptotic structure in banach spaces

被引：0
作者：
Gonzalo, R.
Jaramillo, J. A.
Troyanski, S. L.
机构：
[1] Univ Politecn Madrid, Fac Informat, Dept Matemat Aplicada, E-28660 Madrid, Spain
[2] Univ Complutense Madrid, Fac Ciencias Matemat, Dept Math Anal, E-28040 Madrid, Spain
[3] Bulgarian Acad Sci, Inst Math & Informat, BU-1113 Sofia, Bulgaria
[4] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain
来源：
JOURNAL OF CONVEX ANALYSIS | 2007年 / 14卷 / 02期
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D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study the connections between moduli of asymptotic convexity and smoothness of a Banach space, and the existence of high order differentiable bump functions or equivalent norms on the space. The existence of a high order uniformly differentiable bump function is related to an asymptotically uniformly smooth renorming of power type. On the other hand, the asymptotic uniform convexity of power type is related to the existence of high order smoothness of Nakano sequence spaces.
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页码：249 / 269
页数：21
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