Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

Essential spectra of operators in the class $ \mathcal{B}_n(\Omega)$


Author: Karim Seddighi
Journal: Proc. Amer. Math. Soc. 87 (1983), 453-458
MSC: Primary 47A53; Secondary 47B38
DOI: https://doi.org/10.1090/S0002-9939-1983-0684638-2
MathSciNet review: 684638
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a connected open subset $ \Omega $ of the plane and $ n$ a positive integer, let $ {\mathcal{B}_n}(\Omega )$ be the space introduced by Cowen and Douglas in their paper Complex Geometry and Operator Theory. Our paper deals with characterizing the essential spectrum of an operator $ T$ in $ {\mathcal{B}_n}(\Omega )$ for which $ \sigma (T) = \bar \Omega $ and the point spectrum of $ {T^ * }$ is empty. This class of operators forms an important part of $ {\mathcal{B}_n}(\Omega )$ denoted by $ {\mathcal{B}'_n}(\Omega )$. We use this characterization to give another proof of the result of Axler, Conway and McDonald on determining the essential spectrum of the Bergman operator.

Let $ {A_n}(G) = \left\{ {S:T = {S^ * }{\text{is}}\;{\text{in}}{{\mathcal{B}'}_n}({G^ * })} \right\}$. We also characterize the weighted shifts in $ {A_1}(G)$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A53, 47B38

Retrieve articles in all journals with MSC: 47A53, 47B38


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0684638-2
Keywords: Essential spectrum, Bergman operator, weighted shift
Article copyright: © Copyright 1983 American Mathematical Society