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2006•Guangxi kexueRequires access

k-Nearly Uniformly Smooth Banach Spaces

Cuiling Wang

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Abstract

In this paper,the notion of k-nearly uniformly smooth Banach spaces is introduced,which is a generalization of nearly uniformly smooth Banach spaces,and it is proved that k-nearly uniformly smooth spaces and k-nearly uniformly convex spaces are the dual notions;every k-nearly uniformly smooth spaces is reflexive;one characterization of k-nearly uniformly smooth Banach spaces is given;finally,it is proved that k-uniformly smooth spaces imply(k+1)-nearly uniformly smooth spaces,but its converse is not necessarily true.

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What this paper is about

In this paper,the notion of k-nearly uniformly smooth Banach spaces is introduced,which is a generalization of nearly uniformly smooth Banach spaces,and it is proved that k-nearly uniformly smooth spaces and k-nearly uniformly convex spaces are the dual notions;every k-nearly uniformly smooth spaces is reflexive;one characterization of k-nearly uniformly smooth Banach spaces is given;finally,it is proved that k-uniformly smooth spaces imply(k+1)-nearly uniformly smooth spaces,but its converse is not necessarily true.

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Available abstract

In this paper,the notion of k-nearly uniformly smooth Banach spaces is introduced,which is a generalization of nearly uniformly smooth Banach spaces,and it is proved that k-nearly uniformly smooth spaces and k-nearly uniformly convex spaces are the dual notions;every k-nearly uniformly smooth spaces is reflexive;one characterization of k-nearly uniformly smooth Banach spaces is given;finally,it is proved that k-uniformly smooth spaces imply(k+1)-nearly uniformly smooth spaces,but its converse is not necessarily true.

Key concepts: Uniformly convex space, Mathematics, Banach space, Interpolation space, Uniform continuity, Pure mathematics, Reflexive space, Birnbaum–Orlicz space

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