Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-18T00:15:48.811Z Has data issue: false hasContentIssue false
  • English
  • Français

Borel sets and the spectrum of an operator on an F-space

Published online by Cambridge University Press:  14 November 2011

Zbigniew Słodkowski
Zbigniew Słodkowski
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, Warsaw, Poland
Get access Rights & Permissions [Opens in a new window]

Synopsis

It is shown that the spectrum of a linear operator T on a complete linear metric space X is a Borel set. If, in addition, X is locally convex or separable, then the spectrum of T is a Gδσ set.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 90 , Issue 3-4 , 1981 , pp. 257 - 261
Copyright
Copyright © Royal Society of Edinburgh 1981

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

1Kuratowski, K.. Topology (New York & London: Academic; Warszawa: PWN, 1966).Google Scholar
2Schaefer, H. H.. Topological vector spaces (New York: Macmillan; London: Collier–Macmillan, 1966).Google Scholar
3Shields, A. L.. The spectrum of an operator on an F-space. Proc. Roy. Irish Acad. Sect. A 74 (1974), 291–292.Google Scholar