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Continuity of generalized inverses in Banach algebras

Steffen Roch, Bernd Silbermann (1999)

Studia Mathematica

The main topic of the paper is the continuity of several kinds of generalized inversion of elements in a Banach algebra with identity. We introduce the notion of asymptotic generalized invertibility and completely characterize sequences of elements with this property. Based on this result, we derive continuity criteria which generalize the well known criteria from operator theory.

Continuity of the Drazin inverse II

J. Koliha, V. Rakočević (1998)

Studia Mathematica

We study the continuity of the generalized Drazin inverse for elements of Banach algebras and bounded linear operators on Banach spaces. This work extends the results obtained by the second author on the conventional Drazin inverse.

Convergence in the generalized sense relative to Banach algebras of operators and in LMC-algebras

Bruce Barnes (1995)

Studia Mathematica

The notion of convergence in the generalized sense of a sequence of closed operators is generalized to the situation where the closed operators involved are affiliated with a Banach algebra of operators. Also, the concept of convergence in the generalized sense is extended to the context of a LMC-algebra, where it applies to the spectral theory of the algebra.

Convergence of approximation methods for eigenvalue problem for two forms

Teresa Regińska (1984)

Aplikace matematiky

The paper concerns an approximation of an eigenvalue problem for two forms on a Hilbert space X . We investigate some approximation methods generated by sequences of forms a n and b n defined on a dense subspace of X . The proof of convergence of the methods is based on the theory of the external approximation of eigenvalue problems. The general results are applied to Aronszajn’s method.

Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations

Nicolas Bacaër (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Using the min-plus version of the spectral radius formula, one proves: 1) that the unique eigenvalue of a min-plus eigenvalue problem depends continuously on parameters involved in the kernel defining the problem; 2) that the numerical method introduced by Chou and Griffiths to compute this eigenvalue converges. A toolbox recently developed at I.n.r.i.a. helps to illustrate these results. Frenkel-Kontorova models serve as example. The analogy with homogenization of Hamilton-Jacobi equations is emphasized....

Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations

Nicolas Bacaër (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Using the min-plus version of the spectral radius formula, one proves: 1) that the unique eigenvalue of a min-plus eigenvalue problem depends continuously on parameters involved in the kernel defining the problem; 2) that the numerical method introduced by Chou and Griffiths to compute this eigenvalue converges. A toolbox recently developed at I.n.r.i.a. helps to illustrate these results. Frenkel-Kontorova models serve as example. The analogy with homogenization of Hamilton-Jacobi equations...

Corrigendum and addendum: "On the axiomatic theory of spectrum II"

J. Koliha, M. Mbekhta, V. Müller, Pak Poon (1998)

Studia Mathematica

The main purpose of this paper is to correct the proof of Theorem 15 of [4], concerned with the stability of the class of quasi-Fredholm operators under finite rank perturbations, and to answer some open questions raised there.

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