A new concept for block operator matrices: the quadratic numerical range

被引：55
|
作者：
Langer, H
Markus, A
Matsaev, V
Tretter, C [1 ]
机构：
[1] Univ Leicester, Dept Math & Comp Sci, Leicester LE1 7RH, Leics, England
[2] Vienna Univ Technol, Inst Anal & Tech Math, A-1040 Vienna, Austria
[3] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel
[4] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2001年 / 330卷 / 1-3期
基金：
以色列科学基金会;
关键词：
block operator matrix; quadratic numerical range; Schur complement; angular operator; Riccati equation;
D O I：
10.1016/S0024-3795(01)00230-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper a new concept for 2 x 2-block operator matrices - the quadratic numerical range - is studied. The main results are a spectral inclusion theorem, an estimate of the resolvent in terms of the quadratic numerical range, factorization theorems for the Schur complements, and a theorem about angular operator representations of spectral invariant subspaces which implies e,g. the existence of solutions of the corresponding Riccati equations and a block diagonalization. All results are new in the operator as well as in the matrix case. (C) 2001 Elsevier Science Inc. All rights reserved.
引用
收藏
页码：89 / 112
页数：24
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