A Spectral Representation for Bounded Non-Selfadjoint Operators |
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Authors: | Alexandra Cojuhari Jerzy Stochel |
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Affiliation: | 1. Institute of Mathematics, Jagiellonian University, ul. ?ojasiewicza 6, 30348, Cracow, Poland 2. Department of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059, Cracow, Poland
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Abstract: | An integral representation for an arbitrary bounded operator T defined on a Hilbert space ${mathcal{H}}$ is given. The representing measure is in general defined on a Jordan curve surrounding the spectrum of T. It is obtained as a limit, in a certain weak sense, of a family (F r ) of absolutely continuous measures the Radon?CNikodym derivative of which (with respect to the standard Lebesgue measure on the considered Jordan curve) are described explicitly in terms of the operator T and its adjoint T *. |
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