关于Banach空间中单位球面的覆盖问题

On the Problem of Covering the Unit Sphere In A Banach Space

填球常数是一类控制填充单位球内部、互不相交球个数的几何常数,利用此类常数的思想方法,以两种不同的方式研究了Banach空间的单位球面覆盖问题,引入了两个新的几何常数,并进一步给出了两个几何常数分别在有限维Banach空间和无穷维Banach空间中的取值范围.

The packing constant is a kind of constant which controls the number of disjoint balls belonging to the closed unit ball.From the thought and method of such constant,we mainly consider the problem of the unit sphere covered by two means in a Banach space,and introduce the two new geometric constants.Moreover we give range of values of two geometry constants in finite and infinite Banach spaces,respectively.