关于ces_p(E_1,E_2)的k一致凸性

The k-uniformly rotundity of ces_p(E_1,E_2)

讨论了Banach空间的k一致凸性在cesp(E1 ,E2 )中的提升问题 .提出 :对于若干个Banach空间的cesp 乘积 ,当每个空间具有某种性质时 ,诸空间的某种性质并不能提升到其乘积空间上去 .并举例指出 ,对k≥ 2 ,两个k一致凸区间的cesp 乘积并不是k一致凸的 .证明了 ,若Banach空间E1 是k1 一致凸的 ,E2 是k2 一致凸的 ,则其cesp 乘积是 (k1 +k2 - 1 )一致凸的 .

In this paper, the problems about lifting in ces p(E 1,E 2) of Banach space's k-uniformly rotundity were investigated. For several ces p multiplication of Banach space, some characters of these spaces can't be lifted to their multiplication spaces when every space has these characters. For example, for k≥2,there are two k-uniformly rotundity intervals ces p multiplication which are not k-uniformly rotundity. It prives that if Banach space E 1 is k 1-uniformly rotundity, E 2 is k 2-uniformly rotundity, and ces p multiplication is (k 1+k 2-1),uniformly rotundity.