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A stochastic optimal control problem driven by an abstract evolution equationin a separable Hilbert space is considered. Thanks to the identification of themild solution of the state equation as $\nu$-weak Dirichlet process, the valueprocesses is proved to be a real weak Dirichlet process. The uniqueness of thecorresponding decomposition is used to prove a verification theorem. Throughthat technique several of the required assumptions are milder than thoseemployed in previous contributions about non-regular solutions ofHamilton-Jacobi-Bellman equations.

HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition