The effect of perturbations of linear operators on their polar decomposition

The effect of matrix perturbations on the polar decomposition has been studied by several authors and various results are known. However, for operators between infinite-dimensional spaces the problem has not been considered so far. Here, we prove in particular that the partial isometry in the polar...

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Detalles Bibliográficos
Autores principales:	Duong, R., Philipp, F.
Formato:	JOUR
Materias:	Hilbert space Linear operator Perturbation Polar decomposition
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00029939_v145_n2_p779_Duong
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_00029939_v145_n2_p779_Duong
record_format	dspace
spelling	todo:paper_00029939_v145_n2_p779_Duong2023-10-03T13:55:18Z The effect of perturbations of linear operators on their polar decomposition Duong, R. Philipp, F. Hilbert space Linear operator Perturbation Polar decomposition The effect of matrix perturbations on the polar decomposition has been studied by several authors and various results are known. However, for operators between infinite-dimensional spaces the problem has not been considered so far. Here, we prove in particular that the partial isometry in the polar decomposition of an operator is stable under perturbations, given that kernel and range of original and perturbed operator satisfy a certain condition. In the matrix case, this condition is weaker than the usually imposed equal-rank condition. It includes the case of semi-Fredholm operators with agreeing nullities and deficiencies, respectively. In addition, we prove a similar perturbation result where the ranges or the kernels of the two operators are assumed to be sufficiently close to each other in the gap metric. © 2016 American Mathematical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00029939_v145_n2_p779_Duong
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Hilbert space Linear operator Perturbation Polar decomposition
spellingShingle	Hilbert space Linear operator Perturbation Polar decomposition Duong, R. Philipp, F. The effect of perturbations of linear operators on their polar decomposition
topic_facet	Hilbert space Linear operator Perturbation Polar decomposition
description	The effect of matrix perturbations on the polar decomposition has been studied by several authors and various results are known. However, for operators between infinite-dimensional spaces the problem has not been considered so far. Here, we prove in particular that the partial isometry in the polar decomposition of an operator is stable under perturbations, given that kernel and range of original and perturbed operator satisfy a certain condition. In the matrix case, this condition is weaker than the usually imposed equal-rank condition. It includes the case of semi-Fredholm operators with agreeing nullities and deficiencies, respectively. In addition, we prove a similar perturbation result where the ranges or the kernels of the two operators are assumed to be sufficiently close to each other in the gap metric. © 2016 American Mathematical Society.
format	JOUR
author	Duong, R. Philipp, F.
author_facet	Duong, R. Philipp, F.
author_sort	Duong, R.
title	The effect of perturbations of linear operators on their polar decomposition
title_short	The effect of perturbations of linear operators on their polar decomposition
title_full	The effect of perturbations of linear operators on their polar decomposition
title_fullStr	The effect of perturbations of linear operators on their polar decomposition
title_full_unstemmed	The effect of perturbations of linear operators on their polar decomposition
title_sort	effect of perturbations of linear operators on their polar decomposition
url	http://hdl.handle.net/20.500.12110/paper_00029939_v145_n2_p779_Duong
work_keys_str_mv	AT duongr theeffectofperturbationsoflinearoperatorsontheirpolardecomposition AT philippf theeffectofperturbationsoflinearoperatorsontheirpolardecomposition AT duongr effectofperturbationsoflinearoperatorsontheirpolardecomposition AT philippf effectofperturbationsoflinearoperatorsontheirpolardecomposition
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The effect of perturbations of linear operators on their polar decomposition

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