Spectral properties for perturbations of unitary operators

Astaburuaga, M. A.

Autor

Astaburuaga, M. A.

Cortes, V. H.

Título

Spectral properties for perturbations of unitary operators

Revista

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ISSN

0022-247X

ISSN electrónico

1096-0813

Volumen

380

Número de publicación

2

Página inicio

511

Página final

519

Fecha de publicación

2011

Resumen

Consider a unitary operator U-0 acting on a complex separable Hilbert space H. In this paper we study spectral properties for perturbations of U-0 of the type,

U-beta = U(0)e(iK beta),

with K a compact self-adjoint operator acting on H and beta a real parameter. We apply the commutator theory developed for unitary operators in Astaburuaga et al. (2006) [1] to prove the absence of singular continuous spectrum for U-beta. Moreover, we study the eigenvalue problem for U-beta when the unperturbed operator U-0 does not have any. A typical example of this situation corresponds to the case when U-0 is purely absolutely continuous. Conditions on the eigenvalues of K are given to produce eigenvalues for U-beta for both cases finite and infinite rank of K, and we give an example where the results can be applied. (C) 2011 Elsevier Inc. All rights reserved.

Derechos

acceso restringido

Agencia financiadora

Fondecyt

DOI

10.1016/j.jmaa.2011.03.067

Editorial

ACADEMIC PRESS INC ELSEVIER SCIENCE

Enlace

https://doi.org/10.1016/j.jmaa.2011.03.067

https://repositorio.uc.cl/handle/11534/78703

Id de publicación en WoS

WOS:000290067000010

Paginación

9 páginas

Palabra clave

Point spectrum

Unitary operators

Tema ODS

04 Quality Education

Tema ODS español

04 Educación y calidad

Tipo de documento

artículo

Spectral properties for perturbations of unitary operators

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Autor	Astaburuaga, M. A. Cortes, V. H.
Título	Spectral properties for perturbations of unitary operators
Revista	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
ISSN electrónico	1096-0813
Volumen	380
Número de publicación	2
Página inicio	511
Página final	519
Fecha de publicación	2011
Resumen	Consider a unitary operator U-0 acting on a complex separable Hilbert space H. In this paper we study spectral properties for perturbations of U-0 of the type, U-beta = U(0)e(iK beta), with K a compact self-adjoint operator acting on H and beta a real parameter. We apply the commutator theory developed for unitary operators in Astaburuaga et al. (2006) [1] to prove the absence of singular continuous spectrum for U-beta. Moreover, we study the eigenvalue problem for U-beta when the unperturbed operator U-0 does not have any. A typical example of this situation corresponds to the case when U-0 is purely absolutely continuous. Conditions on the eigenvalues of K are given to produce eigenvalues for U-beta for both cases finite and infinite rank of K, and we give an example where the results can be applied. (C) 2011 Elsevier Inc. All rights reserved.
Derechos	acceso restringido
Agencia financiadora	Fondecyt
DOI	10.1016/j.jmaa.2011.03.067
Editorial	ACADEMIC PRESS INC ELSEVIER SCIENCE
Enlace	https://doi.org/10.1016/j.jmaa.2011.03.067 https://repositorio.uc.cl/handle/11534/78703
Id de publicación en WoS	WOS:000290067000010
Paginación	9 páginas
Palabra clave	Point spectrum Unitary operators
Tema ODS	04 Quality Education
Tema ODS español	04 Educación y calidad
Tipo de documento	artículo