Kasprove’s Stabilization and Fredholm Generalized Index Theory

In this chapter, we show that every countably generated Hilbert A-module can be regarded as a complemented submodule of \(H\otimes A\) (in the sense of unitary equivalence), where H is a separable Hilbert space. This is one of the fundamental results of Hilbert \(C^*\) -module theory, which is called Kasprove’s stabilization theorem.