【摘要】 该文引入了两类新的Banach空间,即k接近一致光滑空间和ω接近一致光滑空间,它们分别是Denka Kutzarova所引入的k接近一致凸空间和ω接近一致凸空间的对偶空间.作为主要结果,得到了这两类Banach空间的特征刻画及一些性质,弄清了k一致光滑空间、k接近一致光滑空间、ω接近一致光滑空间,完全k光滑空间和接近一致光滑空间的蕴涵关系.更多还原

【Abstract】 In this paper,we introduce two new classes of Banach spaces:k nearly uniformly smooth spaces andωnearly uniformly smooth spaces,which are the dual notions to k nearly uniformly convex spaces andωnearly uniformly convex spaces respectively,introduced by Denka Kutzarova.We give some characters and properties of these two kinds of Banach spaces. Apart from that we really distinguish the k uniformly smooth spaces,k nearly uniformly smooth spaces,ωnearly uniformly smooth spaces,fully k smooth spaces and nearly uniformly smooth spaces.更多还原