On a type of reproducing kernel Hilbert C*-modules

Given a Hilbert C*-module M and a locally compact Hausdorff group G, we investigate a reproducing kernel semi-inner product C*-module by supplying a positive semi-definite kernel on G taking values in the space of adjointable operators on M. We examine the analogue of the evaluation functions and we establish several topological properties among which are boundedness, compactness and especially continuity.