  In this paper an analytic operator-valued generalized Feynman integral was
studied on a general Wiener space $C_{a,b}[0,T]$. The function space
$C_{a,b}[0,T]$ is induced by the generalized Brownian motion process associated
with continuous functions $a$ and $b$. The existence of the analytic
operator-valued generalized Feynman integral is investigated as an operator
from $L^1(\mathbb R, \nu_{\delta,a})$ to $L^{\infty}(\mathbb R)$ where
$\nu_{\delta,a}$ is a measure on $\mathbb R$ given by \[
d\nu_{\delta,a}=\exp\{\delta \mathrm{Var}(a)u^2\} du, \] and where $\delta>0$
and $\mathrm{Var}(a)$ denotes the total variation of the mean function $a$ of
the generalized Brownian motion process.
