In this paper, we present some new results on partially observed control problems for infinite-dimensional stochastic systems in Hilbert space using a fundamental result of Da Prato and Zabczyk on an infinite-dimensional Kolmogorov operator. We prove the existence of optimal relaxed controls for an infinite-dimensional Zakai equation following a semigroup approach and the theory of measurable selections. This result is also extended to differential inclusion. We also present some necessary conditions of optimality.