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Abstract:

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.

Registro:

Documento: Artículo
Título:The effect of perturbations of linear operators on their polar decomposition
Autor:Duong, R.; Philipp, F.
Filiación:Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, Berlin, 10623, Germany
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
Palabras clave:Hilbert space; Linear operator; Perturbation; Polar decomposition
Año:2017
Volumen:145
Número:2
Página de inicio:779
Página de fin:790
DOI: http://dx.doi.org/10.1090/proc/13252
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v145_n2_p779_Duong

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Citas:

---------- APA ----------
Duong, R. & Philipp, F. (2017) . The effect of perturbations of linear operators on their polar decomposition. Proceedings of the American Mathematical Society, 145(2), 779-790.
http://dx.doi.org/10.1090/proc/13252
---------- CHICAGO ----------
Duong, R., Philipp, F. "The effect of perturbations of linear operators on their polar decomposition" . Proceedings of the American Mathematical Society 145, no. 2 (2017) : 779-790.
http://dx.doi.org/10.1090/proc/13252
---------- MLA ----------
Duong, R., Philipp, F. "The effect of perturbations of linear operators on their polar decomposition" . Proceedings of the American Mathematical Society, vol. 145, no. 2, 2017, pp. 779-790.
http://dx.doi.org/10.1090/proc/13252
---------- VANCOUVER ----------
Duong, R., Philipp, F. The effect of perturbations of linear operators on their polar decomposition. Proc. Am. Math. Soc. 2017;145(2):779-790.
http://dx.doi.org/10.1090/proc/13252