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Transactions of the American Mathematical Society

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



The local spectral behavior of completely subnormal operators

Authors: K. F. Clancey and C. R. Putnam
Journal: Trans. Amer. Math. Soc. 163 (1972), 239-244
MSC: Primary 47B20
MathSciNet review: 0291844
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Abstract: For any compact set $X$, let $C(X)$ denote the continuous functions on $X$ and $R(X)$ the functions on $X$ which are uniformly approximable by rational functions with poles off $X$. Let $A$ denote a subnormal operator having no reducing space on which it is normal. It is shown that a necessary and sufficient condition that $X$ be the spectrum of such an operator $A$ is that $R(X \cap \overline D ) \ne C(X \cap \overline D )$ whenever $D$ is an open disk intersecting $X$ in a nonempty set.

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Keywords: Subnormal operators, hyponormal operators, spectrum, spectral sets, approximation by continuous functions, approximation by rational functions
Article copyright: © Copyright 1972 American Mathematical Society