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A Joint spectral theorem for unbounded normal opertors

Part of: Selfadjoint operator algebras Special classes of linear operators General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

A. B. Patel
A. B. Patel
Affiliation:
Department of Mathematics Sardar Patel UniversityVallabh Vidyanagar-388120, India
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Abstract

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A joint spectral theorem for an n-tuple of doubly commuting unbounded normal operators in a Hilbert space is proved by using the techniques of GB*-algebras.

MSC classification

Secondary: 47A10: Spectrum, resolvent 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.) 46L99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 2 , April 1983 , pp. 203 - 213
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Allan, G. R., ‘On class of locally convex algebras’, Proc. London Math. Soc. (3) 17 (1967), 91–114.CrossRefGoogle Scholar
[2]Bhatt, S. J., ‘A note on generalized B*-algebras’, J. Indian Math. Soc., to appear.Google Scholar
[3]Dieudonné, J., Treatise on analysis Vol II (Academic Press, 1970).Google Scholar
[4]Dixon, P. G., ‘Generalized B*-algebras’, Proc. London Math Soc. (3) 21 (1970), 693–715.CrossRefGoogle Scholar
[5]Dixon, P. G., ‘Unbounded operator algebras’, Proc. London Math. Soc. 23 (1971), 53–6.CrossRefGoogle Scholar
[6]Fuglede, B., ‘A commuting theorem for normal operators’, Proc. Nat. Acad. Sci. U. S. A. 36 (1950), 35–40.CrossRefGoogle Scholar
[7]Harte, R., ‘The spectral mapping theorem in several variables’. Bull. Amer. Math. Soc. 78 (5) (1972), 871–875.CrossRefGoogle Scholar
[8]Hasting, W. W., ‘Commuting subnormal operators simultancously quasisimilar to unilateral shifts’, Illinois J. Math. 22 (3) (1978), 505–519.Google Scholar
[9]Hewitt, E. and Stromberg, K., Real and abstract analysis (Springer-Verlag, Berlin, Heidelberg, New York, 1969).Google Scholar
[10]Rudin, W., Functional analysis (McGraw-Hill, 1970).Google Scholar
[11]Segal, I. E., ‘A noncommutative extension of abstract integration’. Ann. Math. 57 (1959), 401–457.CrossRefGoogle Scholar
[12]Slodkowski, Z. and Zelazko, W., ‘On joint spectra of commuting families of operators’, Studia Math. 50 (1974), 127–148.Google Scholar
[13]Yeadon, F. J., ‘Convergence of measurable operators’, Proc. Cambridge Philos. Soc. 74 (1973), 257–268.CrossRefGoogle Scholar