The Virozub-Matsaev condition and spectrum of definite type for self-adjoint operator functions

Heinz Langer; Matthias Langer; Alexander Markus; Christiane Tretter

doi:10.1007/s11785-007-0032-z

The Virozub-Matsaev condition and spectrum of definite type for self-adjoint operator functions

Heinz Langer, Matthias Langer, Alexander Markus, Christiane Tretter

Department of Mathematics

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

5 Scopus citations

Abstract

We establish sufficient conditions for the so-called Virozub-Matsaev condition for twice continuously differentiable self-adjoint operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-adjoint operators in Krein spaces and to quadratic operator polynomials are given.

Original language	English
Pages (from-to)	99-134
Number of pages	36
Journal	Complex Analysis and Operator Theory
Volume	2
Issue number	1
DOIs	https://doi.org/10.1007/s11785-007-0032-z
State	Published - 1 Mar 2008

Keywords

Numerical range
Self-adjoint operator function
Spectrum

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s11785-007-0032-z

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title = "The Virozub-Matsaev condition and spectrum of definite type for self-adjoint operator functions",

abstract = "We establish sufficient conditions for the so-called Virozub-Matsaev condition for twice continuously differentiable self-adjoint operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-adjoint operators in Krein spaces and to quadratic operator polynomials are given.",

keywords = "Numerical range, Self-adjoint operator function, Spectrum",

author = "Heinz Langer and Matthias Langer and Alexander Markus and Christiane Tretter",

note = "Funding Information: M. Langer greatly acknowledges the support of the Nuffield Foundation, Grant No. NAL/01159/G. M. Langer and H. Langer thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for its hospitality. C. Tretter gratefully acknowledges the support of Deutsche Forschungsgemeinschaft, DFG, under Grant No. TR368/6-1.",

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doi = "10.1007/s11785-007-0032-z",

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T1 - The Virozub-Matsaev condition and spectrum of definite type for self-adjoint operator functions

AU - Langer, Heinz

AU - Langer, Matthias

AU - Markus, Alexander

AU - Tretter, Christiane

N1 - Funding Information: M. Langer greatly acknowledges the support of the Nuffield Foundation, Grant No. NAL/01159/G. M. Langer and H. Langer thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for its hospitality. C. Tretter gratefully acknowledges the support of Deutsche Forschungsgemeinschaft, DFG, under Grant No. TR368/6-1.

PY - 2008/3/1

Y1 - 2008/3/1

N2 - We establish sufficient conditions for the so-called Virozub-Matsaev condition for twice continuously differentiable self-adjoint operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-adjoint operators in Krein spaces and to quadratic operator polynomials are given.

AB - We establish sufficient conditions for the so-called Virozub-Matsaev condition for twice continuously differentiable self-adjoint operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-adjoint operators in Krein spaces and to quadratic operator polynomials are given.

KW - Numerical range

KW - Self-adjoint operator function

KW - Spectrum

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U2 - 10.1007/s11785-007-0032-z

DO - 10.1007/s11785-007-0032-z

M3 - Article

AN - SCOPUS:43449117813

SN - 1661-8254

VL - 2

SP - 99

EP - 134

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

IS - 1

ER -

The Virozub-Matsaev condition and spectrum of definite type for self-adjoint operator functions

Abstract

Keywords

ASJC Scopus subject areas

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