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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 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"). In the 1970s the theory was extended to non-commutative C *-algebras independently by William Lindall Paschke and Marc Rieffel, the latter in a paper which used Hilbert C *-modules to construct a theory of induced representations of C *-algebras. Hilbert C *-modules are crucial to Kasparov's formulation of KK-theory, 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. == Definitions == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hilbert C*-module」の詳細全文を読む スポンサード リンク
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