On the spectral picture of an irreducible subnormal operator

Author:
Paul McGuire

Journal:
Proc. Amer. Math. Soc. **104** (1988), 801-808

MSC:
Primary 47B20; Secondary 47A10

DOI:
https://doi.org/10.1090/S0002-9939-1988-0964860-2

MathSciNet review:
964860

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Abstract: This paper extends the following result of R. F. Olin and J. E. Thomson: A compact subset of the plane is the spectrum of an irreducible subnormal operator if and only if has exactly one nontrivial Gleason part such that is the closure of . The main result of this paper is that the only additional requirement needed for the pair to be the spectrum and essential spectrum, respectively, is that be a compact subset of which contains the boundary of . Additionally, results are obtained on the question of which index values can be specified on the various components of the complement of .

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0964860-2

Article copyright:
© Copyright 1988
American Mathematical Society