广义von Neumann常数的几何性质

Geometric Properties of Generalized Von Neumann Constant

空间几何常数是空间几何性质的一种量化。为了进一步应用几何常数研究Banach空间的几何结构,通过引入一个新的广义von Neumann常数,给出了广义von Neumann常数的连续性、对称性、有界性以及广义von Neumann常数的等价形式,并用其判别了Banach空间的一致非方性,通过两个例子给出几个特殊Banach空间的广义Von Neumann常数的计算式或估值。

Spatial geometric constant is a quantization of the properties of spatial geometry.In order to further apply the geometric constant to study the geometry of the Banach space,a new generalized von Neumann constant is introduced.We give the continuity,symmetry,boundedness and the equivalent form of the generalized von Neumann constant,and judge the consistent non-square of the Banach space,and give the calculation formula or valuation of several special Banach space with two examples.