Linearization, factorization, and the spectral compression of a self-adjoint analytic operator function under the condition (VM)

H. Langer; A. Markus; V. Matsaev

doi:10.1007/978-3-0348-0221-5

Linearization, factorization, and the spectral compression of a self-adjoint analytic operator function under the condition (VM)

H. Langer, A. Markus, V. Matsaev

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

2 Scopus citations

Abstract

In this paper we continue the study of spectral properties of a selfadjoint analytic operator function A(z) under the Virozub-Matsaev condition. As in [6], [7], main tools are the linearization and the factorization of A(z). We use an abstract definition of a so-called Hilbert space linearization and show its uniqueness, and we prove a generalization of the well-known factorization theorem from [10]. The main results concern properties of the compression A_δ(z) of A(z) to its spectral subspace, called spectral compression of A(z). Close connections between the linearization, the inner linearization, and the local spectral function of A(z) and of its spectral compression A_δ(z) are established.

Original language	English
Title of host publication	A Panorama of Modern Operator Theory and Related Topics
Subtitle of host publication	The Israel Gohberg Memorial Volume
Publisher	Springer Basel
Pages	445-463
Number of pages	19
ISBN (Electronic)	9783034802215
ISBN (Print)	9783034802208
DOIs	https://doi.org/10.1007/978-3-0348-0221-5
State	Published - 1 Jan 2012

Keywords

Factorization
Linearization
Self-adjoint analytic operator function
Spectral function
Spectrum of definite type

ASJC Scopus subject areas

Mathematics (all)

Access to Document

10.1007/978-3-0348-0221-5

Cite this

@inbook{149c0c0140fc409ca024298ef872e423,

title = "Linearization, factorization, and the spectral compression of a self-adjoint analytic operator function under the condition (VM)",

abstract = "In this paper we continue the study of spectral properties of a selfadjoint analytic operator function A(z) under the Virozub-Matsaev condition. As in [6], [7], main tools are the linearization and the factorization of A(z). We use an abstract definition of a so-called Hilbert space linearization and show its uniqueness, and we prove a generalization of the well-known factorization theorem from [10]. The main results concern properties of the compression Aδ(z) of A(z) to its spectral subspace, called spectral compression of A(z). Close connections between the linearization, the inner linearization, and the local spectral function of A(z) and of its spectral compression Aδ(z) are established.",

keywords = "Factorization, Linearization, Self-adjoint analytic operator function, Spectral function, Spectrum of definite type",

author = "H. Langer and A. Markus and V. Matsaev",

year = "2012",

month = jan,

day = "1",

doi = "10.1007/978-3-0348-0221-5",

language = "English",

isbn = "9783034802208",

pages = "445--463",

booktitle = "A Panorama of Modern Operator Theory and Related Topics",

publisher = "Springer Basel",

}

Linearization, factorization, and the spectral compression of a self-adjoint analytic operator function under the condition (VM). / Langer, H.; Markus, A.; Matsaev, V.

A Panorama of Modern Operator Theory and Related Topics: The Israel Gohberg Memorial Volume. Springer Basel, 2012. p. 445-463.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Linearization, factorization, and the spectral compression of a self-adjoint analytic operator function under the condition (VM)

AU - Langer, H.

AU - Markus, A.

AU - Matsaev, V.

PY - 2012/1/1

Y1 - 2012/1/1

N2 - In this paper we continue the study of spectral properties of a selfadjoint analytic operator function A(z) under the Virozub-Matsaev condition. As in [6], [7], main tools are the linearization and the factorization of A(z). We use an abstract definition of a so-called Hilbert space linearization and show its uniqueness, and we prove a generalization of the well-known factorization theorem from [10]. The main results concern properties of the compression Aδ(z) of A(z) to its spectral subspace, called spectral compression of A(z). Close connections between the linearization, the inner linearization, and the local spectral function of A(z) and of its spectral compression Aδ(z) are established.

AB - In this paper we continue the study of spectral properties of a selfadjoint analytic operator function A(z) under the Virozub-Matsaev condition. As in [6], [7], main tools are the linearization and the factorization of A(z). We use an abstract definition of a so-called Hilbert space linearization and show its uniqueness, and we prove a generalization of the well-known factorization theorem from [10]. The main results concern properties of the compression Aδ(z) of A(z) to its spectral subspace, called spectral compression of A(z). Close connections between the linearization, the inner linearization, and the local spectral function of A(z) and of its spectral compression Aδ(z) are established.

KW - Factorization

KW - Linearization

KW - Self-adjoint analytic operator function

KW - Spectral function

KW - Spectrum of definite type

UR - http://www.scopus.com/inward/record.url?scp=85029425540&partnerID=8YFLogxK

U2 - 10.1007/978-3-0348-0221-5

DO - 10.1007/978-3-0348-0221-5

M3 - Chapter

AN - SCOPUS:85029425540

SN - 9783034802208

SP - 445

EP - 463

BT - A Panorama of Modern Operator Theory and Related Topics

PB - Springer Basel

ER -

Linearization, factorization, and the spectral compression of a self-adjoint analytic operator function under the condition (VM)

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this