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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

An operator valued function space integral: A sequel to Cameron and Storvick's paper


Authors: G. W. Johnson and D. L. Skoug
Journal: Proc. Amer. Math. Soc. 27 (1971), 514-518
MSC: Primary 28.46
MathSciNet review: 0272974
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Abstract: Recently Cameron and Storvick introduced and studied an operator valued function space integral related to the Feynman integral. The main theorems of their study establish the existence of the function space integral as a weak operator limit of operators defined at the first stage by finite-dimensional integrals. This paper provides a substantial strengthening of their existence theorem giving the function space integrals as strong operator limits rather than as weak operator limits.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0272974-5
PII: S 0002-9939(1971)0272974-5
Keywords: Feynman integral, Wiener integral, operator valued function space integral, Poisson representation, Bochner integral
Article copyright: © Copyright 1971 American Mathematical Society