2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152407We consider modules E over a C*-algebra A which are equipped with a map into A_+ that has the formal properties of a norm. We completely determine the structure of these modules. In particular, we show that if A has no nonzero commutative ideals then every such E must be a Hilbert module. The commutative case is much less rigid: if A = C_0(X) is commutative then E is merely isomorphic to the module of continuous sections of some bundle of Banach spaces over X. In general E will embed in a direct sum of modules of the preceding two types.16 pages, TeXFunctional AnalysisOperator Algebrastext