Modules with norms which take values in a C*-algebra

Details Modules with norms which take values in a C*-algebra Modules with norms which take values in a C*-algebra

1996-12-19

arxiv.org/abs/funct-an/9612005v1

Mathematics

Operator Algebras

16 pages, TeX

Scientific paper

We 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.

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