## The local spectral behavior of completely subnormal operators

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- by K. F. Clancey and C. R. Putnam
- Trans. Amer. Math. Soc.
**163**(1972), 239-244 - DOI: https://doi.org/10.1090/S0002-9947-1972-0291844-5
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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.## References

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## Bibliographic Information

- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**163**(1972), 239-244 - MSC: Primary 47B20
- DOI: https://doi.org/10.1090/S0002-9947-1972-0291844-5
- MathSciNet review: 0291844