We establish a general framework on the reduced dimensional channel state information (CSI) estimation and pre-beamformer design for frequency-selective massive multiple-input multiple-output (MIMO) systems employing single-carrier (SC) modulation in time division duplex (TDD) mode by exploiting the joint angle-delay domain channel sparsity in millimeter (mm) wave frequencies. First, based on a generic subspace projection taking the joint angle-delay power profile and user-grouping into account, the reduced-rank minimum mean square error (RR-MMSE) instantaneous CSI estimator is derived for spatially correlated wideband MIMO channels. Second, the statistical pre-beamformer design is considered for frequency-selective SC massive MIMO channels. We examine the dimension reduction problem and subspace (beamspace) construction on which the RR-MMSE estimation can be realized as accurately as possible. Finally, a spatio-temporal domain correlator-type reduced-rank channel estimator, as an approximation of the RR-MMSE estimate, is obtained by carrying out least square (LS) estimation in a proper reduced dimensional beamspace. Simulation results for time-varying channels and a number of adaptive filtering techniques with subspace dimension reduction will be illustrated.