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Necessary and sufficient conditions for spectral sets

Published online by Cambridge University Press:  17 April 2009

Takayuki Furuta  and
Muneo Chō
Takayuki Furuta
Affiliation:
Department of Mathematics, Hirosaki University, Bunkyo-Cho 3 Hirosaki, Aomori-Ken 036, Japan.
Muneo Chō
Affiliation:
Department of Mathematics, Hirosaki University, Bunkyo-Cho 3 Hirosaki, Aomori-Ken 036, Japan.
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Abstract

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We shall show necessary and sufficient conditions for which closed set X in the complex plane is a spectral set of an operator T on a complex Hilbert space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 3 , December 1981 , pp. 349 - 355
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Lebow, Arnold, “On von Neumann's theory of spectral sets”, J. Math. Anal. Appl. 7 (1963), 64–90.CrossRefGoogle Scholar
[2]von Neumann, Johann, “Eine Spektraltheorie für allegemeine Operatoren eines unitären Raumes”, Math. Nachr. 4 (1950/1951), 258–281.CrossRefGoogle Scholar
[3]Riesz, Frédéric et Sz.-Nagy, Béla, Legons d'analyse fonetionelle (Akadémiai Kiadó, Budapest, 1952).Google Scholar