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C~m空间中非线性Lipschitz连续算子的定量性质
引用本文:王利生,徐宗本.C~m空间中非线性Lipschitz连续算子的定量性质[J].数学学报,1999,42(6):0-1118.
作者姓名:王利生  徐宗本
作者单位:西安交通大学理学院信息与系统科学研究所,西安,710049
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.

关 键 词:非线性Lipschitz算子  算子逼近距离  乘幂压缩  数值值域  谱集

Quantitative Study of Nonlinear Lipschitz Operators in C~m Space
Wang Lisheng,Xu Zongben.Quantitative Study of Nonlinear Lipschitz Operators in C~m Space[J].Acta Mathematica Sinica,1999,42(6):0-1118.
Authors:Wang Lisheng  Xu Zongben
Affiliation:Wang Lisheng; Xu Zongben(Researeh Center for Applied Mathematics and institute for Information and System Science,Xi'an Jiaotong University, Xi'an 710049, P. R. China)(E-mail: lsh_wang@hotmail.com)
Abstract: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.
Keywords:Nonlinear Lipschitz operator  Operator aproximate distance  Spectrum  Numerical range  Exponential contraction
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