Triple variational principles for self-adjoint operator functions

被引：6

作者：

Langer, Matthias ^{[1
]}

Strauss, Michael ^{[2
]}

机构：

[1] Univ Strathclyde, Dept Math & Stat, 26 Richmond St, Glasgow G1 1XH, Lanark, Scotland

[2] Univ Sussex, Dept Math, Falmer Campus, Brighton BN1 9QH, E Sussex, England

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2016年 / 270卷 / 06期

基金：

英国工程与自然科学研究理事会;

关键词：

Variational principles for eigenvalues; Operator functions; Spectral decomposition; EIGENVALUE PROBLEM; MINIMAX PRINCIPLE; DEFINITE TYPE; KREIN SPACES; SPECTRUM; MATRICES; SYSTEMS; GAPS;

D O I：

10.1016/j.jfa.2015.09.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a very general class of unbounded self-adjoint operator functions we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum. These upper bounds are given by triple variations. Furthermore, we find conditions which imply that a point is in the resolvent set. For norm resolvent continuous operator functions we show that the variational inequality becomes an equality. (C) 2016 The Authors. Published by Elsevier Inc.

引用

页码：2019 / 2047

页数：29

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