【摘要】 本文讨论了完全 k 凸与局部完全 k 凸之间的关系,它包含了 Polak 和 Sims 的结果.此外我们还给出局部一致凸空间的两个新特征,这些特征刻划了 LUR,L-kR 和 Lk-UR 之间的关系.更多还原

【Abstract】 In this paper,we obtian that for each k≥1,there exists a fully(k+1)-convex Banach space which is not locally fully k-convex.It is a more exactdescription for the relationship between fully k-convex and locally fully k-convex and is generalization of result by T.Polak and B.Sims.Also,it ensu-resthat for each k≥1,there exists a Banach space which is fully(k+1)-convex but is not locally k uniform rotund(k uniform rotund).In this paper,we give two new characterization of LUR:A Banach space is LUR if andonly if it is strictly convex,locally k uniform rotund and has(WM)proper-ty or it is locally fully k-convex and has(WM)property.更多还原