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

 

A note on meromorphic operators


Author: Christoph Schmoeger
Journal: Proc. Amer. Math. Soc. 133 (2005), 511-518
MSC (2000): Primary 47A10, 47A11
Published electronically: August 4, 2004
MathSciNet review: 2093075
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Abstract: Let $X$ be a complex Banach space and $T$ a bounded linear operator on $X$. $T$ is called meromorphic if the spectrum $\sigma(T)$ of $T$is a countable set, with $0$ the only possible point of accumulation, such that all the nonzero points of $\sigma(T)$ are poles of $(\lambda I-T)^{-1}$. By means of the analytical core $K(T)$ we give a spectral theory of meromorphic operators. Our results are a generalization of some results obtained by Gong and Wang (2003).


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Additional Information

Christoph Schmoeger
Affiliation: Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Email: christoph.schmoeger@math.uni-karlsruhe.de

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07619-1
PII: S 0002-9939(04)07619-1
Keywords: Meromorphic operators, analytical core
Received by editor(s): August 15, 2003
Received by editor(s) in revised form: October 20, 2003
Published electronically: August 4, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society