Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T08:50:26.495Z Has data issue: false hasContentIssue false
  • English
  • Français

The spectra of Fredholm operators in locally convex spaces

Published online by Cambridge University Press:  24 October 2008

P. A. Olagunju  and
T. T. West
P. A. Olagunju
Affiliation:
University of Ibadan and St John's College, Cambridge
T. T. West
Affiliation:
University of Ibadan and St John's College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

1. Notation and definitions. In this paper necessary and sufficient conditions are found for the spectrum of a Fredholm operator in a locally convex space (always taken to be Hausdorff) to lie on the non-negative real axis of the complex plane. Some results of Grothendieck(2) allow us to obtain the results in this general form; an interesting special case is the trace-class of operators in a general Banach space. We also deal with the case of Hilbert–Schmidt operators in a Hilbert space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 4 , October 1964 , pp. 801 - 806
Copyright
Copyright © Cambridge Philosophical Society 1964

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

REFERENCES

(1)Grommer, J.Ganze transzendente Funktionen mit lauter reellen Nullstellen. J. Reine Angew. Math. 144 (1914), 114–165.CrossRefGoogle Scholar
(2)Grothendieck, A.Produits tensoriels topologiques et espaces nucléaires. Mem. American Math. Soc. 16 (1955), 140 pp.Google Scholar
(3)Hellinger, E. and Toeplitz, O. Integralgleichungen und Gleichungen mit unendlichvielen Unbekannten, from Encyklopädie der Mathematischen Wissenschaften, Band II, 3. Teil, 2. Hälfte (Leipzig, 1927).Google Scholar
(4)Ringrose, J. R.Precompact linear operators in locally convex spaces. Proc. Cambridge Philos. Soc. 53 (1957), 581–591.CrossRefGoogle Scholar
(5)Schatten, R.Norm ideals of completely continuous operators (Berlin, 1960).Google Scholar
(6)Wermer, J.Uniform approximation and maximal ideal spaces. Bull. American Math. Soc. 68(1962), 298–305.CrossRefGoogle Scholar