The stability radius of linear operator pencils

Badea, C.; Mbekhta, M.

Type de document :

Article dans une revue scientifique: Article original

URL permanente :

http://hdl.handle.net/20.500.12210/122128

Titre :

The stability radius of linear operator pencils

Auteur(s) :

Badea, C. [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Mbekhta, M. [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

Journal of Mathematical Analysis and Applications

Pagination :

159-172

Éditeur :

Elsevier

Date de publication :

2001

ISSN :

0022-247X

Discipline(s) HAL :

Mathématiques [math]/Analyse fonctionnelle [math.FA]

Résumé en anglais : [en]

Let T and S be two bounded linear operators from Banach spaces X into Y and suppose that T is Fredholm and the stability number k(T;S) is 0. Let d(T;S) be the supremum of all r > 0 such that dim N(T-\\lambda S) and codim ...
Lire la suite >Let T and S be two bounded linear operators from Banach spaces X into Y and suppose that T is Fredholm and the stability number k(T;S) is 0. Let d(T;S) be the supremum of all r > 0 such that dim N(T-\\lambda S) and codim R(T-\\lambda S) are constant for all \\lambda with |\\lambda | < r. It was proved in 1980 by H. Bart and D.C. Lay that d(T;S) = \\lim_{n\\to\\infty}\\gamma_{n}(T;S)^{1/n}, where \\gamma_{n}(T;S) are some non-negative (extended) real numbers. For X=Y and S = I, the identity operator, we have \\gamma_{n}(T;S) = \\gamma (T^n), where \\gamma is the reduced minimum modulus. A different representation of the stability radius is obtained here in terms of the spectral radii of generalized inverses of T. The existence of generalized resolvents for Fredholm linear pencils is also considered.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Non spécifiée

Vulgarisation :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T15:14:59Z

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