Let C denote the category of Hilbert modules which aresimilar to contractive Hilbert modules. It is proved that if H0, H ∈ C and if H1 is similar to an isometric Hilbertmodule, then the sequence0 → H0 → H → H1 → 0splits. Thus the isometric Hilbert modules are projective inC. It follows that ExtnC (K, H) = 0, whenevern 1, for H, K ∈ C. In addition, it is proved that(Hilbert modules similar to) unitary Hilbert modules are projectivein the category H of all Hilbert modules. Connections withthe conjecture that C is a proper subset ofH are discussed.
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