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

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- by G. W. Johnson and D. L. Skoug PDF
- Proc. Amer. Math. Soc.
**43**(1974), 141-148 Request permission

## 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.## References

- John A. Beekman and Ralph A. Kallman,
*Gaussian Markov expectations and related integral equations*, Pacific J. Math.**37**(1971), 303–317. MR**308353** - 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**0236347**, DOI 10.1512/iumj.1969.18.18041 - G. W. Johnson and D. L. Skoug,
*Operator-valued Feynman integrals of finite-dimensional functionals*, Pacific J. Math.**34**(1970), 415–425. MR**268728**

## Additional Information

- © Copyright 1974 American Mathematical Society
- 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