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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the spectral picture of an irreducible subnormal operator
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by Paul McGuire PDF
Proc. Amer. Math. Soc. 104 (1988), 801-808 Request permission

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 $\mathcal {R}(K)$ 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 $\left \{ {K,{K_e}} \right \}$ 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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Additional Information
  • © Copyright 1988 American Mathematical Society
  • 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