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

M. Langer; Heinz 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

M. Langer, Heinz Langer, Alexander Markus, Christiane Tretter

Mathematics And Statistics

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

5 Citations (Scopus)

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
Publication status	Published - Mar 2008

Keywords

self-adjoint operator function
numerical range
spectrum
Virozub–Matsaev condition

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10.1007/s11785-007-0032-z

DIFFERENTIAL OPERATORS WITH SINGULARITIES AND INDEFINITE INNER PRODUCT SPACES
Langer, M.
Project: Research

Cite this

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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.",

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author = "M. Langer and Heinz Langer and Alexander Markus and Christiane Tretter",

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

AU - Langer, M.

AU - Langer, Heinz

AU - Markus, Alexander

AU - Tretter, Christiane

PY - 2008/3

Y1 - 2008/3

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 - self-adjoint operator function

KW - numerical range

KW - spectrum

KW - Virozub–Matsaev condition

U2 - 10.1007/s11785-007-0032-z

DO - 10.1007/s11785-007-0032-z

M3 - Article

VL - 2

SP - 99

EP - 134

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

SN - 1661-8254

IS - 1

ER -

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

Abstract

Keywords

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DIFFERENTIAL OPERATORS WITH SINGULARITIES AND INDEFINITE INNER PRODUCT SPACES

Cite this