PULLBACK DIAGRAM OF HILBERT MODULES OVER H*-ALGEBRAS

In this paper, we generalize the construction of a pullback diagram in the framework of Hilbert modules over H*-algebras. More precisely we prove that if a commutative diagram of Hilbert H*-modules and morphisms [GRAPHICS] is pullback and Psi(2) is a surjection, then (i) Psi(1) is a surjection and (ii) k e r Phi(1) boolean AND ker Psi(1) = {0} : Conversely, if (i) and (ii) hold, psi(1) (tau(A(1))) is tau(A) -closed and Psi(2) is injective, then the above diagram is pullback.