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High order smoothness and asymptotic structure in banach spaces


Gonzalo, R. and Jaramillo Aguado, Jesús Ángel and Troyanski, S.L. (2007) High order smoothness and asymptotic structure in banach spaces. Journal of Convex Analysis, 14 (2). pp. 249-269. ISSN 0944-6532

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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.

Item Type:Article
Uncontrolled Keywords:Smoothness; bump functions; rough functions; Orlicz spaces
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16614

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