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The spectrum and eigenspaces of a meromorphic operator-valued function

Published online by Cambridge University Press:  14 November 2011

Robert Magnus
Robert Magnus
Affiliation:
The University Science Institute, Dunhaga 3, 107-Reykjavik., Iceland
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Synopsis

It is shown how to associate eigenvectors with a meromorphic mapping defined on a Riemann surface with values in the algebra of bounded operators on a Banach space. This generalises the case of classical spectral theory of a single operator. The consequences of the definition of the eigenvectors are examined in detail. A theorem is obtained which asserts the completeness of the eigenvectors whenever the Riemann surface is compact. Two technical tools are discussed in detail: Cauchy-kernels and Runge's Approximation Theorem for vector-valued functions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 5 , 1997 , pp. 1027 - 1051
Copyright
Copyright © Royal Society of Edinburgh 1997

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