Projective Hilbert A(D)-Modules
نویسندگان
چکیده
Let C denote the category of Hilbert modules which are similar to contractive Hilbert modules. It is proved that if H0, H ∈ C and if H1 is similar to an isometric Hilbert module, then the sequence 0 → H0 → H → H1 → 0 splits. Thus the isometric Hilbert modules are projective in C. It follows that ExtC (K, H) = 0, whenever n > 1, for H, K ∈ C. In addition, it is proved that (Hilbert modules similar to) unitary Hilbert modules are projective in the category H of all Hilbert modules. Connections with the conjecture that C is a proper subset of H are discussed.
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