Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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
MathSciNet review: 964860
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B20, 47A10

Retrieve articles in all journals with MSC: 47B20, 47A10

Additional Information

PII: S 0002-9939(1988)0964860-2
Article copyright: © Copyright 1988 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia