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The spectrum and eigenspaces of a meromorphic operator-valued function
Published online by Cambridge University Press: 14 November 2011
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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