A Note on Full Countably Generated Hilbert Modules

Abstract.

Let E be a full Hilbert module over a pro-C*-algebra A. We prove that if E and E*, the ”dual module” of E, are countably generated in the multiplier module, then the Hilbert A-modules $H \otimes A$ and $H \otimes E$, where H is an infinite dimensional separable Hilbert space, are unitarily equivalent, as well as the Hilbert $A \otimes {\mathcal K}$-modules $A \otimes {\mathcal K}$ and $E \otimes {\mathcal K}$, where ${\mathcal K}$ is the C*-algebra of all compact operators on H.