陕西师范大学学报（自然科学版）2011，Vol.39Issue(2)：17-22,6.
单值延拓性质与广义(ω)性质
The single valued extension property and generalized property (ω)
摘要
Abstract
The generalized property (ω1 ) and generalized property (ω) for a bounded linear operator T defined on a Banach space are studied. A sufficient and necessary condition for an operator to nave the generalized property (ω) is given by means of single-valued extension property( SVEP). It is proved that if T has the SVEP at all points λ(￠)A σSBF+ - (T) , then T satisfies the generalized property (ω) if and only if one of the following conditions is satisfied: (1) there exists n∈ N such that H0 (T-λ) = N[ ( T-λ)n] for every λ ∈ E( T) ; (2) there exists n∈ N such that R[( T-λ)n] is closed for every λ∈E( T) ; (3) there exists n∈N such that K( T-λ) =R[(T-λ)n] for every λ ∈ E( T) ; (4) there exists n∈ N such that γ( Tn) is discontinuous at every λ∈ E (T); (5) des (T-λ)<∞ for every λ∈E( T) ; (6) E(T) =π(T) , where E( T) and ;π( T) denote the set of eigenvalues of T in isolated points of σ( T) and the set of polars.关键词
广义(ω1)性质/广义(ω)性质/单值延拓性质/谱Key words
generalized property (ω1)/ generalized property (ω)/ single valued extension property/ spectrum分类
数理科学引用本文复制引用
戴磊,曹小红..单值延拓性质与广义(ω)性质[J].陕西师范大学学报（自然科学版）,2011,39(2):17-22,6.基金项目
国家自然科学基金资助项目(10726043) （10726043）
中央高校基本科研业务费专项资金项目(GK200901015). （GK200901015）
