On an infinite-dimensional version of the Kreiss matrix theorem
Method of orthogonal projections and approximation of the spectrum of a bounded operator
Correction to "Method od orthogonal projections and approximation of the spectrum of a bounded operator" Studia Math. 65 (1979), 21-29
Method of orthogonal projections and approximation of the spectrum of a bounded operator II
Perturbation of the spectrum οf an essentially selfadjoint operator
The aim of this paper is to find estimates of the Hausdorff distance between the spectra of two nonselfadjoint operators. The operators considered are assumed to have their imaginary parts in some normed ideal of compact operators. In the case of the classical Schatten ideals the estimates are given explicitly.
Matrices splitting the norm and their applications in the theory of stability of difference schemes
In a finite-dimensional real or complex linear normed space X there are characterized all the sets of operators A1,...,An which sum up to the identity operator and such that ||Aix||+...+||Anx|=||x|| for all xX. An example of application in the theory of stability of difference schemes is given.
Determination of eigenvalues and eigenvectors by means of iterations of subspaces
Let A be a compact linear operator in a Banach space X. The author investigates the iterations of a given subspace M of X. He formulates sufficient conditions for the convergence (in the sense of the gap between subspaces). This result is applied to the study of spectra of operators.
Spectra of approximating operators
This is an interesting expository article about the approximation of operators on a complex infinite-dimensional Hilbert space. Although the article does not include research published during the past twenty years or so, it provides a nice account of the stability of the spectrum under approximation (or perturbation). The reader interested in pursuing this area of research might refer to the bibliography in [D. A. Herrero, Approximation of Hilbert space operators. Vol. I, Pitman, Boston, MA, 1982;...
Spectral approximation of positive operators by iteration subspace method
The iteration subspace method for approximating a few points of the spectrum of a positive linear bounded operator is studied. The behaviour of eigenvalues and eigenvectors of the operators arising by this method and their dependence on the initial subspace are described. An application of the Schmidt orthogonalization process for approximate computation of eigenelements of operators is also considered.
Sur les systèmes infinis d'équations différentielles ordinaires dans certains espaces de Fréchet
Table des Matières§ 1. Généralités. Matrices infinies............................................ 5§ 2. Systèmes infinis d'équations différentielles. Problème de Cauchy. Existence-unicité............................................................................ 10§ 3. Approximation par les systèmes finis......................................... 20§ 4. Dépendance de la solution des conditions initiales ou d'un paramètre......... 23§ 5. Quelques remarques sur la séparation des variables..............................
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