Triple variational principles for self-adjoint operator functions

Matthias Langer; Michael Strauss

doi:10.1016/j.jfa.2015.09.004

Triple variational principles for self-adjoint operator functions

Matthias Langer, Michael Strauss

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

36 Downloads (Pure)

Abstract

For a very general class of unbounded self-adjoint operator function 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.

Original language	English
Pages (from-to)	2019-2047
Number of pages	29
Journal	Journal of Functional Analysis
Volume	270
Issue number	6
Early online date	19 Jan 2016
DOIs	https://doi.org/10.1016/j.jfa.2015.09.004
Publication status	Published - 15 Mar 2016

Keywords

variational principles for eigenvalues
operator function
spectral decomposition

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10.1016/j.jfa.2015.09.004Licence: CC BY 4.0

Langer-Strauss-JFA2016-triple-variational-principles-for-self-adjoint-operator-functionsFinal published version, 528 KBLicence: CC BY 4.0

http://www.sciencedirect.com/science/journal/00221236

Matthias Langer
- m.langer@strath.ac.uk
- Mathematics And Statistics - Senior Lecturer
Person: Academic

1 Finished

Spectral Theory of Block Operator Matrices
Langer, M.
EPSRC (Engineering and Physical Sciences Research Council)
1/09/07 → 30/11/09
Project: Research

Cite this

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abstract = "For a very general class of unbounded self-adjoint operator function 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.",

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AB - For a very general class of unbounded self-adjoint operator function 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.

KW - variational principles for eigenvalues

KW - operator function

KW - spectral decomposition

UR - http://www.sciencedirect.com/science/journal/00221236

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JO - Journal of Functional Analysis

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Triple variational principles for self-adjoint operator functions

Abstract

Keywords

Access to Document

Matthias Langer

Spectral Theory of Block Operator Matrices

Cite this