The stability radius of linear operator pencils

Badea, C.; Mbekhta, M.

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

The stability radius of linear operator pencils

Author(s) :

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

Journal title :

Journal of Mathematical Analysis and Applications

Pages :

159-172

Publisher :

Elsevier

Publication date :

2001

ISSN :

0022-247X

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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