Various properties of L2(G;M) the space of the square-integrable M-valued functions on the compact group G where M is a Hilbert C*- module are established. In particular a pre-Hilbert space structure is constructed on it. Similar results are obtained for its discrete analogue via the Fourier transform of vector-valued functions.
Mathematics Subject Classification: 43A77; 43A15; 46C50
Keywords: Hilbert CĄ-module; compact group; Fourier transform; squareintegrable