广义von Neumann常数与正规结构  

Generalized von Neumann constant and normal structures

作　　者：赵亮 赵平安 ZHAO Liang;ZHAO Pingan(College of Science,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨商业大学学报（自然科学版）》2023年第4期431-436,共6页Journal of Harbin University of Commerce：Natural Sciences Edition

摘　　要：为了进一步应用几何常数研究Banach空间的几何结构,通过引入广义von Neumann常数,给出广义von Neumann常数与广义光滑模的关系式;并利用弱收敛序列系数与广义von Neumann常数的关系得到Banach空间具有正规结构的一个充分条件;当λ小于0.5且广义von Neumann常数满足不等式条件时,蕴含Banach空间具有弱正规结构;根据广义von Neumann常数与弱正交序列系数的关系给出Banach空间具有弱正规结构的一个充分条件;最后通过一个例子给出特殊空间的广义von Neumann常数的计算式.In order to further study the geometric structure of Banach space by using geometric constants,the relation between generalized von Neumann constant and the generalized smooth module was given by introducing generalized von Neumann constant;a sufficient condition for Banach space to have normal structure was obtained by using the relationship between weakly convergence sequence coefficient and generalized von Neumann constants;when the generalized von Neumann constant was less than 0.5 and satisfies the inequality condition,the implied Banach space has a weak normal structure;according to the relationship between generalized von Neumann constant and weakly orthogonal sequence coefficients,a sufficient condition for Banach space to have weakly normal structures was given;the computation of the generalized von Neumann constant for a special space was given by an example.

关 键 词：BANACH空间 广义von Neumann常数 弱正交序列系数 广义光滑模 弱正规结构 弱收敛序列系数 

分 类 号：O177.2[理学—数学]