  We consider convolution-type stochastic Volterra equations with additive
Hilbert-valued fractional Brownian motion, $0<H<1$. We find the weak solution
to this stochastic Volterra equation, and study its stochastic integral part,
the stochastic convolution, which we show to be mean-zero Gaussian. We develop
an It\^o isometry for stochastic integrals with respect to a Hilbert-valued
fractional Brownian motion, and use it to compute the covariance of the
stochastic convolution. This formula, which uses fractional integrals and
derivatives, generalizes the well-known formula from the case $H=1/2$.
