Hilbert C-modules are mathematical objects which generalise the notion of a Hilbert space (which itself is a generalisation of Euclidean space), in that they endow a linear space with an "inner product" which takes values in a C-algebra
Hilbert C-modules are mathematical objects which generalise the notion of a Hilbert space (which itself is a generalisation of Euclidean space), in that they endow a linear space with an "inner product" which takes values in a C-algebra. Hilbert C-modules are crucial to Kasparov's formulation of KK-theory,[4] and provide the right framework to extend the notion of Morita equivalence to C-algebras. They can be viewed as the generalization of vector bundles to noncommutative C-algebras and as such play an important role in noncommutative geometry, notably in C-algebraic quantum group theory, and groupoid C*-algebras.
Further reading : Hilbert-Modules
