Hilbert C*-modules are mathematical objects that generalise the notion of Hilbert spaces (which are themselves generalisations of Euclidean space), in that they endow a linear space with an "inner product" that takes values in a C*-algebra. They were first introduced in the work of Irving Kaplansky in 1953, which developed the theory for commutative, unital algebras (though Kaplansky observed that the assumption of a unit element was not "vital").
Hilbert C*-modules are mathematical objects that generalise the notion of Hilbert spaces (which are themselves generalisations of Euclidean space), in that they endow a linear space with an "inner product" that takes values in a C*-algebra. They were first introduced in the work of Irving Kaplansky in 1953, which developed the theory for commutative, unital algebras (though Kaplansky observed that the assumption of a unit element was not "vital").
Source: Wikipedia "Hilbert C*-module" · CC BY-SA 4.0
Share this article: X · Bluesky