自反Banach空间中的一个非线性锥分离定理  

A Nonlinear Cone Separation Theorem in Reflexive Banach Space

作　　者：杨吉英 何青海 YANG Jiying;HE Qinghai(School of Date Science,Baoshan University,Baoshan Yunnan 665000;School of Mathematics and Statistics,Yunnan University,Kunming 650106,China)

机构地区：[1]保山学院大数据学院,云南保山678000 [2]云南大学数学与统计学院,昆明650106

出　　处：《重庆师范大学学报（自然科学版）》2023年第1期129-132,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11371312);云南省应用基础研究项目(No.2017FD140)。

摘　　要：[目的]给出自反Banach空间中闭锥的一个非线性分离定理。[方法]利用已有文献定义的一类广义正线性集中的元的相关性质来证明分离定理。[结果]在没有凸性的假设下,证明了两个具有某种特殊分离性质的闭锥,能够被现有文献中定义的一类具有conic水平集的单调次线性函数的零次水平集逼近,还证明了与它的ε-conic邻域具有分离性质的闭锥也能被这类函数中的某个函数的零次水平集逼近。[结论]自反的Banach空间中两个满足某种分离性质的闭锥,能够被某个次线性函数分离,包含一个锥且被另一个锥所包含的Bishop-phelps锥是存在的。[Purposes]A nonlinear cone separation theorem in reflexive Banach space is proposed.[Methods]The separation theorem is proved by using the correlation properties of the elements of a class of generalized positive linear sets defined in literature.[Findings]Under the assumption of no convexity,it is proved that two closed cones with some special separation property can be approximated by the zeroth level set of a class of monotone sublinear functions with conic level set defined in the existing literature,and that the closed cones with the separation property of its epsilon-conic neighborhood can also be approximated by the zeroth level set of a function of such functions.[Conclusions]In reflexive Banach space,the two closed cones possessing the separation property can be separated by a certain sublinear function,and the question on the existence of a Bishop-Phelps cone which is close to the given cone is positively answered.

关 键 词：广义正线性集 分离逼近 Bishop-phelps锥 

分 类 号：O177[理学—数学]