Common multiples of operator polynomials with analytic coefficients.
Comparison of Norms |||f (A) - f(B) ||| and |||f (|A - B|) |||.
Construction of Non-Linear Local Quantum Processes.
Continuity and general perturbation of the Drazin inverse for closed linear operators.
Convergence of approximation methods for eigenvalue problem for two forms
The paper concerns an approximation of an eigenvalue problem for two forms on a Hilbert space . We investigate some approximation methods generated by sequences of forms and defined on a dense subspace of . 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.
Corrigendum and addendum: "On the axiomatic theory of spectrum II"
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.
Dense range perturbations of hypercyclic operators
We show that if (Tₙ) is a hypercyclic sequence of linear operators on a locally convex space and (Sₙ) is a sequence of linear operators such that the image of each orbit under every linear functional is non-dense then the sequence (Tₙ + Sₙ) has dense range. Furthermore, it is proved that if T,S are commuting linear operators in such a way that T is hypercyclic and all orbits under S satisfy the above non-denseness property then T - S has dense range. Corresponding statements for operators and sequences...
Differentiability of perturbed semigroups and delay semigroups
Suppose that A generates a C₀-semigroup T on a Banach space X. In 1953 R. S. Phillips showed that, for each bounded operator B on X, the perturbation A+B of A generates a C₀-semigroup on X, and he considered whether certain classes of semigroups are stable under such perturbations. This study was extended in 1968 by A. Pazy who identified a condition on the resolvent of A which is sufficient for the perturbed semigroups to be immediately differentiable. However, M. Renardy showed in 1995 that immediate...
Differentiable bundles of subspaces and operators in Banach spaces
Diskrete Approximation von Eigenwertproblemen. I. Qualitative Konvergenz.
Diskrete Approximation von Eigenwertproblemen. II. Konvergenzordnung.
Diskrete Approximation von Eigenwertproblemen. III. Asymptotische Entwicklungen. - Discrete Approximation of Eigenvalue-Problems. III. Asymptotic Expansions.
Diskrete Konvergenz linearer Operatoren. II.
Distinguished Self-Adjoint Extensions of Dirac Operators Constructed by Means of Cutt-Off Potentials.
Domain perturbations, capacity and shift of eigenvalues
After introducing the notion of capacity in a general Hilbert space setting we look at the spectral bound of an arbitrary self-adjoint and semi-bounded operator . If is subjected to a domain perturbation the spectrum is shifted to the right. We show that the magnitude of this shift can be estimated in terms of the capacity. We improve the upper bound on the shift which was given in Capacity in abstract Hilbert spaces and applications to higher order differential operators (Comm. P. D. E., 24:759–775,...
Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator
We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable along the magnetic...
Economical Finite Rank Perturbations of Semi-Fredholm Operators.
Ein neues Surjektivitätskriterium im Hilbertraum.
Ein Störungssatz für abgeschlossene, lineare Operatoren.
Ein Zerlegungssatz für Resolventen elliptischer Operatoren.