Perturbations of Fredholm operators
Perturbations of operators satisfying a local growth condition.
Perturbations of operators similar to contractions and the commutator equation
Let T and V be two Hilbert space contractions and let X be a linear bounded operator. It was proved by C. Foiaş and J. P. Williams that in certain cases the operator block matrix R(X;T,V) (equation (1.1) below) is similar to a contraction if and only if the commutator equation X = TZ-ZV has a bounded solution Z. We characterize here the similarity to contractions of some operator matrices R(X;T,V) in terms of growth conditions or of perturbations of R(0;T,V) = T ⊕ V.
Perturbations of Positive Semigroups and Applications to Population Genetics.
Perturbations of Selfadjoint Operators with Point Spectra by Restrictions and Selfadjoint Extensions.
Perturbations of the H∞-calculus
Suppose A is a sectorial operator on a Banach space X, which admits an H∞-calculus. We study conditions on a multiplicative perturbation B of A which ensure that B also has an H∞-calculus. We identify a class of bounded operators T : X→X, which we call strongly triangular, such that if B = (1 + T) A is sectorial then it also has an H∞-calculus. In the case X is a Hilbert space an operator is strongly triangular if and only if ∑ Sn(T)/n <∞ where (Sn(T))n=1∞ are the singular values of T.
Polaroid type operators and compact perturbations
A bounded linear operator T acting on a Hilbert space is said to be polaroid if each isolated point in the spectrum is a pole of the resolvent of T. There are several generalizations of the polaroid property. We investigate compact perturbations of polaroid type operators. We prove that, given an operator T and ε > 0, there exists a compact operator K with ||K|| < ε such that T + K is polaroid. Moreover, we characterize those operators for which a certain polaroid type property is stable under...
Positivity and stability for a system of transport equations with unbounded boundary perturbations.
Preservation of ergodicity under perturbation (Erratum).
Prolongements maximaux positifs d'opérateurs positifs et problèmes de perturbations singulières
Quasiaffine transforms of operators
We obtain a new sufficient condition (which may be useful elsewhere) that a compact perturbation of a normal operator be the quasiaffine transform of some normal operator. We also give some applications of this result.
Quasibeschränkte Fredholmoperatoren.
Relative boundedness conditions and the perturbation of nonlinear operators
Relative Inversion in der Störungstheorie von Operatoren und ...-Algebren.
Relatively bounded and compact perturbations of th order differential operators.
Remarks on embeddable semigroups in groups and a generalization of some Cuthbert's results.
Remarks on similarity and quasisimilarity of operators
Remarques sur la structure interne des composantes connexes semi-Fredholm
Soit C(X,Y) l’ensemble des opérateurs fermés à domaines denses dans l’espace de Banach X à valeurs dans l’espace de Banach Y, muni de la métrique du gap. Soit et , où α (T) est la dimension du noyau de T. Nous montrons que est un ouvert de (et donc ouvert dans C(X,Y)) et que est dense dans . Nous déduisons quelques résultats de densités. A la fin de se travail nous donnons un exemple d’espace de Banach X tel que, d’une part, n’est pas connexe dans B(X) et d’autre part, l’ensemble des...
Resonances and convergence of perturbation theory for N-body atomic systems in external AC-electric field
Restriction of an operator to the range of its powers
Let T be a bounded linear operator acting on a Banach space X. For each integer n, define to be the restriction of T to viewed as a map from into . In [1] and [2] we have characterized operators T such that for a given integer n, the operator is a Fredholm or a semi-Fredholm operator. We continue those investigations and we study the cases where belongs to a given regularity in the sense defined by Kordula and Müller in[10]. We also consider the regularity of operators with topological...