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Multiparameter problems and joint spectra

Published online by Cambridge University Press:  14 November 2011

D. F. McGhee
D. F. McGhee
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow Gl 1XH, Scotland
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Synopsis

In this paper, we demonstrate an intimate connection between the spectrum of a multiparameter problem and the joint spectrum of an associated set of commuting operators, and show that the spectrum of a multiparameter problem involving bounded operators is non-empty. Multiparameter systems involving compact and self-adjoint operators are considered, and some simplification of results in the literature are noted.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 1-2 , 1982 , pp. 129 - 135
Copyright
Copyright © Royal Society of Edinburgh 1982

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