分块对角算子矩阵在上三角扰动下的精细拟谱和固有拟谱

THE METICULOUS PSEUDO-SPECTRA AND INTRINSIC PSEUDO-SPECTRA FOR 2×2 DIAGONAL BLOCK OPERATOR MATRICES UNDER THE BOUNDED PERTURBATION OF UPPER-TRIANGULAR OPERATOR MATRICES

本文研究了对角分块算子矩阵在上三角有界扰动情形下的精细拟谱和固有拟谱的问题.利用空间分解技巧和算子的扰动原理等方法,将谱的结论推广到拟谱上,获得了对角分块算子矩阵在上三角有界扰动情形下的ε-单射性以及它的拟剩余谱与拟连续谱.最后,刻画了对角分块算子矩阵在上三角有界扰动情形下的固有拟点谱、固有拟剩余谱和固有拟连续谱.

In this paper,we study the problem of meticulous pseudo-spectra and intrinsic pseudo-spectra for the diagonal block operator matrices under the bounded perturbation of upper-triangular operator matrices.By means of space decomposition technique and perturba-tion principle of operators,we extend the spectral result to pseudo-spectrum and obtain theε-injectivity and its pseudo-residual spectrum and pseudo-continuous spectrum for the diagonal block operator matrices with the bounded perturbation of upper-triangular operator matrices.Finally,the intrinsic pseudo-point spectrum,intrinsic pseudo-residual spectrum and intrinsic pseudo-continuous spectrum for the diagonal block operator matrices in the case of the bounded perturbation of upper-triangular operator matrices are described.