  For a class of stochastic delay evolution equations driven by cylindrical
$Q$-Wiener process, we study the Pontryagin's maximum principle for the
stochastic recursive optimal control problem. The delays are given as moving
averages with respect to general finite measures and appear in all the
coefficients of the control system. In particular, the final cost can contain
the state delay. To derive the main result, we introduce a new form of
anticipated backward stochastic evolution equations with terminals acting on an
interval as the adjoint equations of the delayed state equations and deploy a
proper dual analysis between them. Under certain convex assumption on the
coefficient function and the Hamiltonian, we also show sufficiency of the
maximum principle.
