Unbounded operators generated by a given spectral measure |
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Authors: | AR Sourour |
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Institution: | Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1, Canada |
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Abstract: | Let T be a closed densely-defined operator on a Banach space X and let E(·) be a spectral measure whose range is a complete Boolean algebra of projections in X. Then T is of the form ∝f(λ) dE(λ) if and only if T commutes with and leaves invariant every invariant subspace of . |
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