For a class of path-dependent stochastic evolution equations driven by cylindrical $Q$-Wiener process, we study the Pontryagin's maximum principle for the stochastic recursive optimal control problem. In this infinite-dimensional control system, the state process depends on its   past trajectory, the control is delayed via an integral with respect to a general finite measure, and the final cost relies on the delayed state.
To obtain the maximum principle, we introduce a new type of non-anticipative path derivative and its dual operator, which allows us to derive an anticipated backward stochastic evolution equation as the adjoint equation of the state equation. This is joint work with Guomin Liu and Meng Wang.