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Support of the joint spectral measure

Part of: Selfadjoint operator algebras General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Jan Niechwiej  and
R. O. Vyborny
Jan Niechwiej
Affiliation:
Instytut Matematyki, Uniwersytet Jagielloński, ul. Reymonta 4, 30-059 Kraków, Poland
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Abstract

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For a doubly commuting n-tuple of unbounded normal operators in a Hilbert space the joint spectral measure can be constructed and its closed support described as the joint spectrum of the given n-tuple. The same is here shown for larger, possibly uncountable, families of operators.

MSC classification

Secondary: 47A10: Spectrum, resolvent 46L99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 1 , August 1987 , pp. 74 - 80
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Berezanskiĭ, Ju. M., ‘Projective spectral theorem’, Uspehi Mat. Nauk 39 (1984), 3–52, (in Russian); Russian Math. Surveys, 39:4 (1984), 1–62.Google Scholar
[2]Niechwiej, J., ‘On commutative algebras of unbounded operators’, Studia Math. 78 (1984), 217–230.CrossRefGoogle Scholar
[3]Patel, A. B., ‘A joint spectral theorem for unbounded normal operators’, J. Austral. Math. Soc. 34 (1983), 203–213.CrossRefGoogle Scholar
[4]Stone, M. H., ‘On unbounded operators in Hilbert space’, J. Indian Math. Soc. 15 (1951), 155–192.Google Scholar