Slowly oscillating perturbations of periodic Jacobi operators in l²(ℕ)

Marcin Moszyński. "Slowly oscillating perturbations of periodic Jacobi operators in l²(ℕ)." Studia Mathematica 192.3 (2009): 259-279. <http://eudml.org/doc/285017>.

@article{MarcinMoszyński2009,
abstract = {We prove that the absolutely continuous part of the periodic Jacobi operator does not change (modulo unitary equivalence) under additive perturbations by compact Jacobi operators with weights and diagonals defined in terms of the Stolz classes of slowly oscillating sequences. This result substantially generalizes many previous results, e.g., the one which can be obtained directly by the abstract trace class perturbation theorem of Kato-Rosenblum. It also generalizes several results concerning perturbations of the discrete (free or periodic) Schrödinger operator. The paper concerns "one-sided" Jacobi operators (i.e. in l²(ℕ)) and is based on the method of subordinacy. We provide some spectral results for the unperturbed, periodic case, and also an appendix containing some subordination theory tools.},
author = {Marcin Moszyński},
journal = {Studia Mathematica},
keywords = {Jacobi matrix; Jacobi operator; spectral analysis; absolutely continuous spectrum; absolutely continuous operator; pure point spectrum; periodicity; subordinacy; slowly oscillating sequence; perturbation},
language = {eng},
number = {3},
pages = {259-279},
title = {Slowly oscillating perturbations of periodic Jacobi operators in l²(ℕ)},
url = {http://eudml.org/doc/285017},
volume = {192},
year = {2009},
}

TY - JOUR
AU - Marcin Moszyński
TI - Slowly oscillating perturbations of periodic Jacobi operators in l²(ℕ)
JO - Studia Mathematica
PY - 2009
VL - 192
IS - 3
SP - 259
EP - 279
AB - We prove that the absolutely continuous part of the periodic Jacobi operator does not change (modulo unitary equivalence) under additive perturbations by compact Jacobi operators with weights and diagonals defined in terms of the Stolz classes of slowly oscillating sequences. This result substantially generalizes many previous results, e.g., the one which can be obtained directly by the abstract trace class perturbation theorem of Kato-Rosenblum. It also generalizes several results concerning perturbations of the discrete (free or periodic) Schrödinger operator. The paper concerns "one-sided" Jacobi operators (i.e. in l²(ℕ)) and is based on the method of subordinacy. We provide some spectral results for the unperturbed, periodic case, and also an appendix containing some subordination theory tools.
LA - eng
KW - Jacobi matrix; Jacobi operator; spectral analysis; absolutely continuous spectrum; absolutely continuous operator; pure point spectrum; periodicity; subordinacy; slowly oscillating sequence; perturbation
UR - http://eudml.org/doc/285017
ER -