  We characterize the Markovian and affine structure of the Volterra Heston
model in terms of an infinite-dimensional adjusted forward process and specify
its state space. More precisely, we show that it satisfies a stochastic partial
differential equation and displays an exponentially-affine characteristic
functional. As an application, we deduce an existence and uniqueness result for
a Banach-space valued square-root process and provide its state space. This
leads to another representation of the Volterra Heston model together with its
Fourier-Laplace transform in terms of this possibly infinite system of affine
diffusions.
