A Convergence Theorem for Selfadjoint Operators Applicable to Dirac Operators with Cutoff Potentials.
A generalization of Signorini's perturbation method suggested by two problems of Grioli
A model of atomic radiation
A note on preservation of spectra for two given operators
We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the...
A note on the index of -Fredholm operators
From Corollary 3.5 in [Berkani, M; Sarih, M.; Studia Math. 148 (2001), 251–257] we know that if , are commuting -Fredholm operators acting on a Banach space , then is a -Fredholm operator. In this note we show that in general we do not have , contrarily to what has been announced in Theorem 3.2 in [Berkani, M; Proc. Amer. Math. Soc. 130 (2002), 1717–1723]. However, if there exist such that , , , are commuting and , then , where stands for the index of a -Fredholm operator.
A perturbation characterization of compactness of self-adjoint operators
A characterization of compactness of a given self-adjoint bounded operator A on a separable infinite-dimensional Hilbert space is established in terms of the spectrum of perturbations. An example is presented to show that without separability, the perturbation condition, which is always necessary, is not sufficient. For non-separable spaces, another condition on the self-adjoint operator A, which is necessary and sufficient for the perturbation, is given.
A perturbation problem in the presence of affine symmetries
An approach to a local analysis of solutions of a perturbation problem is proposed when the unperturbed operator has affine symmetries. The main result is a local theorem on existence, uniqueness, and analytic dependence on a parameter.
A perturbation theorem for semigroups of linear operators
A Perturbation Theorem for the Essential Spectral Radius of Strongly Continuous Semigroups.
A perturbation theory of resonances
A Remark on Perturbations of Compact Operators.
A rigorous approach to relativistic corrections of bound state energies for spin-1/2 particles
A Spectral Mapping Theorem for Holomorphic Functions.
A spectral mapping theorem for perturbed strongly continuous semigroups.
A spectral mapping theorem for semigroups solving PDEs with nonautonomous past.
A spectral perturbation problem and its applications to waves above an underwater ridge.
A theorem on "localized" self-adjointness of Schrödinger operators with potentials.
A theory on perturbations of the Dirac operator.
A unitary invariant for pairs of self-adjoint operators.
A-Browder-type theorems for direct sums of operators
We study the stability of a-Browder-type theorems for orthogonal direct sums of operators. We give counterexamples which show that in general the properties , , and are not preserved under direct sums of operators. However, we prove that if and are bounded linear operators acting on Banach spaces and having the property , then has the property if and only if , where is the upper semi-B-Weyl spectrum of . We obtain analogous preservation results for the properties , and with...