Spectral inclusion for unbounded block operator matrices
Spectral inclusion for unbounded block operator matrices
复制标题
DOI：
10.1016/j.jfa.2008.12.024
复制
发表时间：
2009-06-01
影响因子：
1.7
通讯作者：
Tretter, Christiane
中科院分区：
文献类型：
--
作者：
Tretter, Christiane
本文建立了无界线性算子A的谱的一个新的解析包络，它容许一个分块算子矩阵表示。对于对角占优和非对角占优块算子矩阵，我们证明了最近引入的二次数值值域W-2（A）包含A的特征值，并且A的近似点谱包含在W-2（A）的闭包中.这为利用非凸集W-2（A）封闭无界分块算子矩阵的谱提供了一种新的方法。几个例子表明，这种谱包含可能是他相当轻比一个通常的数值范围或扰动定理，无论是在非自伴的情况下，在自伴的情况下。应用狄拉克算子和双通道哈密顿。(C)2009 Elsevier Inc. All rights reserved.
In this paper we establish it new analytic enclosure for the spectrum of unbounded linear operators A admitting a block operator matrix representation. For diagonally dominant and off-diagonally dominant block operator matrices, we show that the recently introduced quadratic numerical range W-2(A) contains the eigenvalues of A and that the approximate point spectrum of A is contained in the closure of W-2(A). This provides a new method to enclose the spectrum of unbouded block operator matrices by means of the non-convex set W-2(A). Several examples illustrate that this spectral inclusion may he considerably lighter than the one by the usual numerical range or by perturbation theorems, both in the non-self-adjoint case and in the self-adjoint case. Applications to Dirac operators and to two-channel Hamiltonians are given. (C) 2009 Elsevier Inc. All rights reserved.