k—严格凸与k—UR空间

k-Strict Convexity and k-UR Spaces

中文摘要:

      本文讨论k—严格凸Banach空间的各种性质,并证明,对于有限维空间,k—严格凸与k—UR是等价的.另外若x,Y分别是k₁—严格凸k₂—严格凸的Banach空间,11+k₂-1)—严格凸的Banach空间.

英文摘要:

      The results of this paper are as follow(1) Let X be a finite dimensional Banach space and dim X≥ k. If X is k-strictly convex, then X is k-uniformly rotund.(2) Let X be k₁-strictly convex and let Y be k₂ strictly convex. Then (X⊕Y)_p, is (k₁+k₂-1)-strictly convex.