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–Nikodym 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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Acknowledgments
The research of the second author was partially supported by the Polish Ministry of Science and Higher Education, Grants; NN201546438 and 11.420.04.
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Communicated by Guest Editors L. Littlejohn and J. Stochel.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Cojuhari, A., Stochel, J. A Spectral Representation for Bounded Non-Selfadjoint Operators. Complex Anal. Oper. Theory 6, 819–828 (2012). https://doi.org/10.1007/s11785-011-0198-2
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DOI: https://doi.org/10.1007/s11785-011-0198-2