Banach空间中弱收敛序列系数的估计

Some Estimates for the Weakly Convergent Sequence Coefficient in Banach Spaces

利用.Jordan—von Neumann型常数C_t~′（X）,C_（-∞）（X）和弱正交系数μ（X）对Banach空间中的弱收敛序列系数WCS（X）进行了估计,从而得到空间具有正规结构的充分条件,这些结论推广了最近一些文献中的结果.同时,还计算了Bynum空间l_（2.∞）。中上述常数的取值,来说明我们给定的条件是一个严格的推广.

We establish two inequalities concerning the weakly convergent sequence WCS（X） and Jordan-yon Neumann type constants Ct（X）, C-∞（X）, which enable us to obtain some sufficient conditions for normal structure. The results obtained in this paper represent an extension as well as refinement of previous known results. Meanwhile, the Jordan-von Neumann type constants Ct（X）, C-∞（X） for the Bynum space l2∞ are computed, and are used to show that our results are sharp.