Glasnik Matematicki, Vol. 36, No.2 (2001), 263-269.

A NOTE ON BLECHER'S CHARACTERIZATION OF HILBERT C^*-MODULES

Franka Miriam Brückler

Abstract.   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 H_V, such that V can be embedded in the algebra B(H, H_V) of bounded operators between H and H_V. In this paper it is shown: 1. For a Hilbert C*-module over a C*-algebra of compact operators the Hilbert space H_V 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, H_V).

1991 Mathematics Subject Classification.   46L08.