A note on Blecher's characterization of Hilbert C* -modules

By a theorem of D. P. Blecher, a Hilbert C*-module V over a C*-algebra A (faithfully and nondegenerately represented on a Hilbert space H) is characterized by a certain Hilbert space HV, such that V can be embedded in the algebra B(H, HV) of bounded operators between H and HV. In this paper it is shown: 1. For a Hilbert C*-module over a C*-algebra of compact operators the Hilbert space HV conicides with a Hilbert subspace of the module, which characterizes all adjointable operators on the module; 2. For any Hilbert C*-module V, its strict completion can be realized in the algebra B(H, HV).