排序方式: 共有4条查询结果,搜索用时 15 毫秒
1
1.
CHENG LiXin SHI HuiHua & ZHANG Wen School of Mathematical Sciences Xiamen University Xiamen China 《中国科学A辑(英文版)》2009,(9)
A normed space is said to have ball-covering property if its unit sphere can be contained in the union of countably many open balls off the origin. This paper shows that for every ε>0 every Banach space with a w*-separable dual has a 1+ε-equivalent norm with the ball covering property. 相似文献
2.
Rn空间中单位球面覆盖的半径问题 总被引:2,自引:0,他引:2
Banach空间X中的一个闭球族B是X的球覆盖,如果B中的任一元素不包含原点作为其内点,且B中元素之并覆盖了X的单位球面炙.一个球覆盖B称为是极小的当且仅当B的势小于或等于X中所有球覆盖的势.文献[1]证明了在R^n中球覆盖的极小势为n+1,本文重点利用文献[4]所给出的n维空间中n-单形与其外接超球面间的若干关系,证明了在有限维欧氏空间R^n中极小球覆盖的最小半径为n/2,且当极小球覆盖中(n+1)个球的球心恰好为球面詈&的内接正则n-66单形的顶点时可以取到. 相似文献
3.
This paper presents two counterexamples about ball-coverings of Banach spaces and shows a new characterization of uniformly non-square Banach spaces via ball-coverings. 相似文献
4.
By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it admits a ball-covering consisting of countably many balls. This paper, by constructing the equivalent norms on l~∞, shows that ball-covering property is not invariant under isomorphic mappings, though it is preserved under such mappings if X is a Gateaux differentiability space; presents that this property of X is not heritable by its closed subspaces; and the property is also not preserved under quotient mappings. 相似文献
1