Some Absolutely Continuous Operators I (Classic Reprint) - Tapa blanda

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Excerpt from Some Absolutely Continuous Operators I
Most likely these conditions could be established for a wider class of operators, e.g. For the operator -a q, A being the Laplacian and the function q satisfying the povsner-ikebe condition Another example could be the operator M K, M being the multiplication operator and K satisfying a gentleness condition introduced by Friedrichs or a condition of partial gentleness introduced by the author, else where At present, however, we are not concerned with these questions.
In conclusion let us remark that C. R. Putnam formulated a condition for the absolute continuity of normal operators. His condition involved the commutator of the given operator and of an operator to be constructed Let us also remark that the notion of an absolutely continuous operator was extended to operators which may not admit a spectral resolution. Speci fically Sz. Nagy [a] assigned to an arbitrary contraction opera tor a unitary transformation, which in turn, he used to assign an operator valued measure to the contraction. Later M.
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