有界线性算子的摄动定理  

Perturbation Theorem for Bounded Linear Operator

作　　者：曹小红[1] 郭懋正[1] 孟彬[1] 

机构地区：[1]北京大学数学科学学院应用数学实验室,北京100871

出　　处：《数学学报（中文版）》2004年第2期259-264,共6页Acta Mathematica Sinica：Chinese Series

摘　　要：本文研究了正则算子的摄动理论.考虑Banach空间X上的正则算子T,假设dim[K(T)∩N(T)]<∞且K(T)闭,则当S∈B(X)可逆,ST=TS,‖S‖充分小时,证明了T—S为上半Fredholm算子.在以上条件下,若K(T)+N(T)或者R(T)+N(T)在X中有有限维的补子空间,这时T—S为Fredholm算子.If T is a regular operator on a Banach space X, with finite dimensional intersection K(T) ∩ N(T) and K(T) closed, and if 5 is invertible, commutes with T and has sufficiently small norm, then T - S is an upper semi-Fredholm operator. If in addition K(T) + N(T) or R(T) + N(T) has a complementary subspace with finite dimension, then T ?S is a Fredholm operator.

关 键 词：正则算子 单值扩张性质 半FREDHOLM算子 

分 类 号：O177.2[理学—数学]