Hilbert C*-module

Summary

A Hilbert C*-module over a C*-algebra $A$ is a module over $A$ with an inner product. The values of this inner product lie in $A$ instead of in $\C$. It generalizes a Hilbert space, which is the case $A = \C$. Hilbert modules are the basic tool of Kasparov's KK-theory and of Morita equivalence of C*-algebras.