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An Integral Representation for the Product of Spectral Measures

Published online by Cambridge University Press:  20 November 2018

N. A. Derzko
N. A. Derzko*
Affiliation:
University of Toronto, Toronto, Ontario
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Let be a Hilbert space with inner product (•, •) and let E(•) and E0(•) be spectral measures in corresponding to self-adjoint operators and . In this paper we consider the set function ƒ(I × J) = E(I)E0(J) defined on the semiring of bounded rectangles, and obtain an integral representation for this set function for disjoint I, J under the hypotheses that H — H0 is a type of Carleman operator.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 904 - 912
Copyright
Copyright © Canadian Mathematical Society 1968

References

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