线性算子的广义谱

Generalized Spectrum of Linear Operators

在复赋范线性空间上线性算子广义逆概念的基础上引入线性算子广义谱概念,讨论了复数λ为有界线性算子T的广义谱的充要条件,得出了关于线性算子广义谱的两个恒等式,证明了有界线性算子广义谱的谱映照定理.

The definition of generalized spectrum of linear operator T on complex normed linear spaces was introduced;the necessary and sufficient condition that λ is the generalized spectrum of operator T was discussed;two identities about generalized spectrum of operators were obtained;the generalized spectrum theorem for the linear bound operators was proved.