I am reading about Gaussian measure on infinite dimensional spaces in Bogachev's Gaussian Measures (1998) - Chapter 2. In it, the notion of Gaussian measure on a locally convex space $X$ is given in Definition 2.2.1, and Theorem 2.3.1 proves the existence of Gaussian measures on separable Hilbert spaces.
My question is about the existence of Gaussian measures on more generalized spaces, for example, on separable Banach spaces. I have been looking up to other references, but so far, I haven't found any better result than the existence on Hilbert space.