关于连续线性算子广义预解集的某些结果

袁国常

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (7) : 1020-1025.

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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (7) : 1020-1025. DOI: 10.12341/jssms09239
论文

关于连续线性算子广义预解集的某些结果

    袁国常
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Some Results on the Generalized Resolvent Set of the Continuous Linear Operators

    YUAN Guochang
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摘要

讨论了Banach 空间上连续线性算子T 的广义预解集的相关结果,证明了:若λ0∈ρG(T), 当~|λ−λ0|<γ(Tλ0) 时,
λ∈ρG(T); 与~λ∈ρG(T) 等价的条件:当~Tn→T,0∈ρG(Tn),则 0\in\rho_G(T);以及T的柱心 C_O(T)$ 在数量扰动下的不变性.

Abstract

In this paper, some results on the generalized resolvent set of the continuous linear operators are discussed. It is shown that λ∈ρG(T) as
|λ−λ0|<γ(Tλ0) for λ0∈ρG(T), and an equivalent condition about λ∈ρG(T) is obtained. Moreover, if Tn→T,0∈ρG(Tn), then 0∈ρG(T); the invariance of core CO(T) of T is proved
under quantity preturbation.

关键词

连续线性算子 / 广义预解集 / 有界齐性投影 / 柱心 / 约化极小模.

Key words

Continuous linear operator / generalized resolvent set / bounded homogeneous projection / core / reduced minimum modulus.

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袁国常. 关于连续线性算子广义预解集的某些结果. 系统科学与数学, 2010, 30(7): 1020-1025. https://doi.org/10.12341/jssms09239
YUAN Guochang. Some Results on the Generalized Resolvent Set of the Continuous Linear Operators. Journal of Systems Science and Mathematical Sciences, 2010, 30(7): 1020-1025 https://doi.org/10.12341/jssms09239
中图分类号： 47A05    47A10   
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