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 | References | Similar Articles | Additional Information
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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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1988-0964860-2
Article copyright:
© Copyright 1988
American Mathematical Society