(C-K)性质在两类序列空间中的提升

GEOMETRIC PROPERTY (C-K)CAN BE LIFTED TO SEQUENCE SPACES l^p(E_i) AND ces_p(E)

讨论了(C-K)(K=Ⅰ,Ⅱ,Ⅲ)性质在两类序列空间lp(Ei)和cesp(E)中的提升问题,证明了(C-K)(K=Ⅰ,Ⅱ,Ⅲ)性质可以提升到lp(Ei)和cesp(E),并给出了cesp(E)(1<p<∞)紧局部完全w凸及弱紧局部完全w凸的判据.

In this paper,the lifting problems in the sequence spaces l^p(E_i) and ces_p(E) are discussed,and it is proved that: (1) Geometric property (C-K)(K=Ⅰ,Ⅱ ,Ⅲ)can be lifted to sequence spaces (l^p(E_i)) and ces_p(E), (2) One necessary and sufficient condition for sequence spaces ces_p(E) to be CLwR spaces (resp.WCLwR spaces) is obtained.