کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4591729 | 1335049 | 2009 | 24 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Spectral inclusion for unbounded block operator matrices Spectral inclusion for unbounded block operator matrices](/preview/png/4591729.png)
In this paper we establish a 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 W2(A) contains the eigenvalues of A and that the approximate point spectrum of A is contained in the closure of W2(A). This provides a new method to enclose the spectrum of unbounded block operator matrices by means of the non-convex set W2(A). Several examples illustrate that this spectral inclusion may be considerably tighter 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.
Journal: Journal of Functional Analysis - Volume 256, Issue 11, 1 June 2009, Pages 3806-3829