  Path-dependent PDEs (PPDEs) are natural objects to study when one deals with
non Markovian models. Recently, after the introduction of the so-called
pathwise (or functional or Dupire) calculus (see [15]), in the case of
finite-dimensional underlying space various papers have been devoted to
studying the well-posedness of such kind of equations, both from the point of
view of regular solutions (see e.g. [15, 9]) and viscosity solutions (see e.g.
[16]). In this paper, motivated by the study of models driven by path-dependent
stochastic PDEs, we give a first well-posedness result for viscosity solutions
of PPDEs when the underlying space is a separable Hilbert space. We also
observe that, in contrast with the finite-dimensional case, our well-posedness
result, even in the Markovian case, applies to equations which cannot be
treated, up to now, with the known theory of viscosity solutions.
