Hostname: page-component-788cddb947-nxk7g Total loading time: 0 Render date: 2024-10-19T10:45:31.608Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Atkinson, F. V.. Multiparameter Eigenvalue Problems (New York: Academic Press, 1972).Google Scholar
2Arens, R. and Calderon, A. P.. Analtyic functions of several Banach algebra elements. Ann. of Math. 62 (1955), 204–216.CrossRefGoogle Scholar
3Bunce, J.. Characters on single generated C*-algebras. Proc. Amer. Math. Soc. 25 (1970), 297–303.Google Scholar
4Bunce, J.. The joint spectrum of commuting non-normal operators. Proc. Amer. Math. Soc. 29 (1971), 499–505.Google Scholar
5Dash, A. T.. Joint spectra. Studia Math. 45 (1973), 225–237.Google Scholar
6Dixmier, J.. Les Algebres d'Operateurs dans l'espace Hilbertien (Gauthier-Villars, Paris: 1957).Google Scholar
7Halmos, P. R.. Lecture notes on Operator Theory, Summer School on Banach Algebra and Operator Theory, University of Newcastle (1976).Google Scholar
8Källström, A.. and Sleeman, B. D.. Solvability of a linear operator system. J. Math. Appl. 55 (1976), 785–793.Google Scholar
9McGhee, D. F. and Roach, G. F.. The spectrum of multiparameter problems in Hilbert space. Proc. Roy. Soc. Edinburgh Sect. A 91 (1981), 31–42.Google Scholar
10Sleeman, B. D.. Multiparameter Spectral Theory in Hilbert Space (London: Pitman, 1978).CrossRefGoogle Scholar
11Taylor, J. L.. A joint spectrum for several commuting operators. J. Functional Anal. 6 (1970), 172–191.Google Scholar