Projective Hilbert A ( D )
نویسندگان
چکیده
Jim Williams died in 1983. The surviving three authors are pleased to dedicate this paper to his memory. Abstract. Let C denote the category of Hilbert modules which are similar to con-tractive Hilbert modules. It is proved that if H 0 ; H 2 C and if H 1 is similar to an isometric Hilbert module, then the sequence 0 ! H 0 ! H ! H 1 ! 0 splits. Thus the isometric Hilbert modules are projective in C. It follows that Ext n C (K;H) = 0, whenever n > 1, for H; K 2 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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