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- Hilbert_C*-module abstract "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.".
- Hilbert_C*-module wikiPageExternalLink hilmod.html.
- Hilbert_C*-module wikiPageID "16059132".
- Hilbert_C*-module wikiPageRevisionID "596304735".
- Hilbert_C*-module hasPhotoCollection Hilbert_C*-module.
- Hilbert_C*-module title "Hilbert C*-Module".
- Hilbert_C*-module urlname "HilbertC-Star-Module".
- Hilbert_C*-module subject Category:C*-algebras.
- Hilbert_C*-module subject Category:Operator_theory.
- Hilbert_C*-module subject Category:Theoretical_physics.
- Hilbert_C*-module comment "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").".
- Hilbert_C*-module label "Hilbert C*-module".
- Hilbert_C*-module label "Hilbert-C*-Modul".
- Hilbert_C*-module sameAs Hilbert-C*-Modul.
- Hilbert_C*-module sameAs m.03qmxns.
- Hilbert_C*-module sameAs Q5761182.
- Hilbert_C*-module sameAs Q5761182.
- Hilbert_C*-module wasDerivedFrom Hilbert_C*-module?oldid=596304735.
- Hilbert_C*-module isPrimaryTopicOf Hilbert_C*-module.