C^m空间中非线性Lipschitz连续算子的定量性质  

Quantitative Study of Nonlinear Lipschitz Operators in C^m Space

作　　者：王利生[1] 徐宗本[1] 

机构地区：[1]西安交通大学理学院信息与系统科学研究所,西安710049

出　　处：《数学学报（中文版）》1999年第6期1111-1118,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金

摘　　要：在有限维复Ｂａｎａｃｈ空间Ｃｍ中，全体Ｌｉｐｓｃｈｉｔｚ连续算子构成一赋半范的非线性算子空间Ｌ（Ｃｍ）．本文研究Ｌ（Ｃｍ）中非线性算子的定量性质，包括：Ｌ（Ｃｍ）中可逆算子到不可逆算子集合的逼近距离、Ｌ（Ｃｍ）中算子乘幂压缩的逆问题以及Ｌ（Ｃｍ）中算子的数值值域与谱集的联系，文中所得结果推广了线性算子理论中许多著名结论．All nonlinear Lipschitzian operators in Cm space constitute a seminormoperator space L(Cm). In this paper, many important properties of operator in L(Cm)are studied, include: the approximate distance from a invertable operator to the setof noninvertable operators, the converse of exponential contraction of operator, therelation between numerical range and spectrum of operator. The obtained resultsgeneralize many famous theorems of lineax operator.

关 键 词：复巴拿赫空间 李普希兹算子 非线性算子 

分 类 号：O177.91[理学—数学]