一个非线性算子逼近定理及其应用  

An Approximation Theorem of Nonlinear Operator and its Application

作　　者：陈白丽[1] 王利生[1] 王亘[1] 

机构地区：[1]西安交通大学

出　　处：《西安交通大学学报》1999年第4期91-93,共3页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金

摘　　要：设Ｌ（Ｃｍ）表示Ｃｍ中非线性Ｌｉｐｓｃｈｉｔｚ算子全体所构成的赋半范算子空间，Ｍ表示Ｌ（Ｃｍ）中不可逆算子所组成的集合．文中证明：对任何非Ｍ中的Ｌｉｐｓｃｈｉｆｙ算子Ｔ，Ｔ到Ｍ的最佳逼近距离恰为Ｔ的ｇｌｂＬｉｐｓｃｈｉｔｚ数．所获结果推广了著名的线性算子逼近定理，并成功用于精确刻画非线性Ｌｉｐｓｃｈｉｔｚ算子族谱集的包含域．Let L(C m ) be a semi normal space composed of all nonlinear Lipschitzian continuous operators on C m , and M a set of all non invertable operators in L(C m ). It is proved that for any T in L (C m) , the best approximation distance from T to M is the glb Lipschitz constant of T . This result generalizes an approximation theorem of linear operator, and applies to the exact characterization of inclusion region for spectrum of nonlinear operator.

关 键 词：算子逼近 李普希兹算子 非线性算子 最佳逼近 

分 类 号：O174.41[理学—数学] O177.91[理学—基础数学]