Abstract
A «CGS-property» for the spectral measures is introduced and the classical results of determining complete systems of unitary invariants for self-adjoint and bounded normal operators on separable Hilbert spaces are extended to the class of spectral measures with this property. As a consequence, the above mentioned results are extended to unbounded normal operators on separable Hilbert spaces. Moreover, three different kinds of multiplicity are defined and it is shown that for the measures with the «CGS-property» they all coincide. In the last section some analogues of the multiplicity functions defined by Stone [14] are related to the total multiplicity.
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Supported by the C.D.C.H.T. project C-409 of the Universidad de Los Andes, Mérida, Venezuela.
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Panchapagesan, T.V. Unitary invariants of spectral measures with the CGS-property. Rend. Circ. Mat. Palermo 42, 219–248 (1993). https://doi.org/10.1007/BF02843946
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DOI: https://doi.org/10.1007/BF02843946