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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
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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

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References

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