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Transactions of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0291844-5
PII: S 0002-9947(1972)0291844-5
Keywords: Subnormal operators, hyponormal operators, spectrum, spectral sets, approximation by continuous functions, approximation by rational functions
Article copyright: © Copyright 1972 American Mathematical Society