k-β and k-Nearly Uniformly Convex Banach Spaces
نویسنده
چکیده
vol. 162, No. 2, 1991 k-β and k-Nearly Uniformly Convex Banach Spaces Denka Kutzarova Different uniform geometrical properties have been defined between the uniform convexity and the reflexivity of Banach spaces. In the present paper we introduce other properties of this type, namely k-β and k-nearly uniform convexity. The definitions, as well as some of the results presented here, are announced in [7]. Sullivan [24] has defined k-uniformly rotund Banach spaces which by a suggestion of Davis are all superreflexive. Fan and Glicksberg [1] have introduced fully k-convex Banach spaces. Let x1, . . . , xk+1 be vectors in a Banach space X. The k-dimensional volume enclosed by x1, . . . , xk+1 is given by V (x1, x2, . . . , xk+1)
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