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 for a class of finite-dimensional functionals . Here we consider a space of not necessarily finite-dimensional functionals generated by the earlier functionals. We show that is a Banach space and recognize as the direct sum of more familiar Banach spaces. We also show that the function space integral exists for . In contrast we give an example of an such that does not exist.

**[1]**John A. Beekman and Ralph A. Kallman,*Gaussian Markov expectations and related integral equations*, Pacific J. Math.**37**(1971), 303-318. MR**0308353 (46:7467)****[2]**R. H. Cameron and D. A. Storvick,*An operator valued function space integral and a related integral equation*, J. Math. Mech.**18**(1968), 517-552. MR**38**#4643. MR**0236347 (38:4643)****[3]**G. W. Johnson and D. L. Skoug,*Operator-valued Feynman integrals of finite-dimensional functionals*, Pacific J. Math.**34**(1970), 415-425. MR**42**#3625. MR**0268728 (42:3625)**

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Additional Information

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