Banach空间的U凸系数

U-Convex Coefficient of Banach Space

空间几何常数是空间几何性质的量化,从几何性质的研究到几何常数的计算是从定性到定量的推进。首先引入了一个新的几何常数U凸系数,并研究了它与一致非方和正规结构等几何性质之间的关系,并且通过研究它与常数R(X)的关系,得到Banach空间X弱接近一致光滑,且具有不动点性质。其次利用它与弱正交系数之间的关系给出了Banach空间具有正规结构的充分条件。最后给出了U凸模在l_p序列空间的计算。

The spatial geometric constant is the quantification of the geometrical properties of space. From the study of geometric properties to the calculation of geometric constants from qualitative to quantitative advancement. Firstly, this paper introduces a new geometric constant U-convex coefficient. Studying its relationship with geometric properties such as uniform non-square and regular structures and by studying its relationship with constants, the Banach space is weakly close to uniform smooth and has fixed point properties. Secondly, Using the relationship between it and weak orthogonal coefficients gives a sufficient condition for Banach spaces to have a regular structure. Finally, the calculation of the convex model in the sequence space is given.