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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On subnormal operators

Author: Mehdi Radjabalipour
Journal: Trans. Amer. Math. Soc. 211 (1975), 377-389
MSC: Primary 47B20
MathSciNet review: 0377574
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Abstract: Let T be the adjoint of a subnormal operator defined on a Hilbert space H. For any closed set $ \delta $, let $ {X_T}(\delta ) = \{ x \in H$: there exists an analytic function $ {f_x}:{\text{C}}\backslash \delta \to H$ such that $ (z - T){f_x}(z) \equiv x\} $. It is shown that T is decomposable (resp. normal) if $ {X_T}(\partial {G_\alpha })$ is closed (resp. if $ {X_T}(\partial {G_\alpha }) = \{ 0\} )$ for a certain family $ \{ {G_\alpha }\} $ of open sets. Some of the results are extended to the case that T is the adjoint of the restriction of a spectral or decomposable operator to an invariant subspace.

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Keywords: Hilbert space, normal operator, spectral operator, subnormal operator, decomposable operator, spectral subspace
Article copyright: © Copyright 1975 American Mathematical Society