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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A function space integral for a Banach space of functionals on Wiener space


Authors: G. W. Johnson and D. L. Skoug
Journal: Proc. Amer. Math. Soc. 43 (1974), 141-148
MSC: Primary 28A40; Secondary 46G10
DOI: https://doi.org/10.1090/S0002-9939-1974-0340536-X
MathSciNet review: 0340536
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Abstract: In an earlier paper the authors established the existence of Cameron and Storvick's function space integral $ {J_q}(F)$ for a class of finite-dimensional functionals $ F$. Here we consider a space $ A$ of not necessarily finite-dimensional functionals generated by the earlier functionals. We show that $ A$ is a Banach space and recognize $ A$ as the direct sum of more familiar Banach spaces. We also show that the function space integral $ J_q^{{\text{an}}}(F)$ exists for $ F \in A$. In contrast we give an example of an $ {F_0} \in A$ such that $ J_q^{{\text{seq}}}({F_0})$ does not exist.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0340536-X
Keywords: Wiener integral, operator valued function space integral, Feynman integral, Banach space
Article copyright: © Copyright 1974 American Mathematical Society