平均一致凸Banach空间的最小范数控制  

The minimal norm control problem in averagely uniformly convex Banach spaces

作　　者：樊丽颖[1] 武俊峰[2] 

机构地区：[1]哈尔滨理工大学应用数学系,哈尔滨150080 [2]哈尔滨理工大学自动化系,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2009年第3期306-310,共5页Journal of Natural Science of Heilongjiang University

基　　金：教育部科技计划重点项目(206041)

摘　　要：讨论平均凸性与Banach空间某些重要几何性质的关系,证明平均弱局部一致凸的Banach空间具有(WM)性质;平均一致凸的Banach空间具有Banach-Saks性质;平均一致凸的Banach空间具有正规结构,从而具有不动点性质。作为应用,研究平均一致凸Banach空间中分布参数系统的最小范数控制问题。The relationship between average convexities and some geometric properties of Banach spaces is discussed. It is proved that averagely weakly locally uniformly convex Banach spaces have （WM） property; averagely uniformly convex Banach spaces have Banach- Saks property and the normal structure. Hence an averagely uniformly convex Banach space has the fixed point property. Meanwhile, the minimal norm control problem of the input distributed parameter system is investigated in averagely uniformly convex Banach spaces.

关 键 词：平均一致凸 正规结构 Banach—Saks性质 最小范数控制 

分 类 号：N941.4[自然科学总论—系统科学] N117.0