Methods of abstract harmonic analysis in the perturbation of linear operators
Copyright policy )Methods of abstract harmonic analysis in the perturbation of linear operators
The basic results of the paper refer to questions of similarity of a certain class of non-self-adjoint operators. Methods of abstract harmonic analysis for operators from certain group algebras connected with an unperturbed operator are used. Applications are criteria for the spectrality of perturbed spectral operators with discrete spectrum, strengthening results of J. Schwarz and H. P. Kramer, results of the asymptotics of eigenvalues, results of the convergence of spectral expansions of perturbed operators, results on the similarity of a special class of operators and other results.
similarity of certain classes of non-self-adjoint operators, unperturbed operator, Perturbation theory of linear operators, group algebras, Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), spectral theory of Banach modules over Banach algebras, Spectral operators, decomposable operators, well-bounded operators, etc., abstract harmonic analysis, asymptotics of eigenvalues, Representations of commutative topological algebras, spectrality of perturbed spectral operators with discrete spectrum, Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis), similarity of a certain class of non-self-adjoint operators, convergence of spectral expansions of perturbed operators, spectral properties of perturbations of spectral operators
similarity of certain classes of non-self-adjoint operators, unperturbed operator, Perturbation theory of linear operators, group algebras, Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), spectral theory of Banach modules over Banach algebras, Spectral operators, decomposable operators, well-bounded operators, etc., abstract harmonic analysis, asymptotics of eigenvalues, Representations of commutative topological algebras, spectrality of perturbed spectral operators with discrete spectrum, Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis), similarity of a certain class of non-self-adjoint operators, convergence of spectral expansions of perturbed operators, spectral properties of perturbations of spectral operators
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