线性算子束谱的一些性质刻画

摘要

研究了希尔伯特空间上算子束的特性.利用算子谱理论及空间分解的技巧,通过构造算子矩阵的方法,得到线性算子束Aλ+B谱的性质及Aλ+B的非正规性的充分必要条件.%Let(Yf)be separable Hilbert spaces and(A,B)be a given pair of operators in B(ye).Some properties of the spectrumσ(λA + B)ofλA + B is considered and the necessary and sufficient conditions have been obtained for Aλ + B to be non-regular by using the method of block operator construction and the theory of operator spectrum.