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 (Fr) 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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