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Self adjoint operators and matrix measures

Published online by Cambridge University Press:  17 April 2009

Patrick J. Browne
Patrick J. Browne
Affiliation:
University of Toronto, Toronto, Canada.
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Abstract

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Given a self adjoint operator, T, on a Hilbert space H, and given an integer n ≥ 1, we produce a collection , N ∈ L, of n × n positive matrix measures and a unitary map U: such that UTU−1, restricted to the co-ordinate space , is the multiplication operator F(t) → tF(t) in that space. This is a generalization of the spectral representation theory of Dunford and Schwartz, Linear operators, II (1966).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 3 , June 1971 , pp. 289 - 305
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Dunford, Nelson and Schwartz, Jacob T., Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space (Interscience [John Wiley & Sons], New York, London, 1963).Google Scholar