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On the Spectral Picture of an Irreducible Subnormal Operator

Paul Mcguire
Proceedings of the American Mathematical Society
Vol. 104, No. 3 (Nov., 1988), pp. 801-808
DOI: 10.2307/2046796
Stable URL: http://www.jstor.org/stable/2046796
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Spectral Picture of an Irreducible Subnormal Operator
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Abstract

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

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