Abstract
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 X2←X1→Ф1→Y1→Y2 is pullback and ψ2 is a surjection, then (i) ψ 1 is a surjection and (ii) kerф1 ∩ ker ψ1 = {0}. Conversely, if (i) and (ii) hold, ψ1(т(A1)) is тA2 -closed and ψ2 is injective, then the above diagram is pullback.
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