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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 wikiPageLength "8908".
- Hilbert_C*-module wikiPageOutDegree "42".
- Hilbert_C*-module wikiPageRevisionID "681363885".
- Hilbert_C*-module wikiPageWikiLink 1953_in_science.
- Hilbert_C*-module wikiPageWikiLink Algebra_over_a_field.
- Hilbert_C*-module wikiPageWikiLink Antilinear_map.
- Hilbert_C*-module wikiPageWikiLink Approximate_identity.
- Hilbert_C*-module wikiPageWikiLink C*-algebra.
- Hilbert_C*-module wikiPageWikiLink C*-algebraic_quantum_group_theory.
- Hilbert_C*-module wikiPageWikiLink C*-algebras.
- Hilbert_C*-module wikiPageWikiLink Category:C*-algebras.
- Hilbert_C*-module wikiPageWikiLink Category:Operator_theory.
- Hilbert_C*-module wikiPageWikiLink Category:Theoretical_physics.
- Hilbert_C*-module wikiPageWikiLink Cauchy-Schwarz_inequality.
- Hilbert_C*-module wikiPageWikiLink Cauchy–Schwarz_inequality.
- Hilbert_C*-module wikiPageWikiLink Closure_(topology).
- Hilbert_C*-module wikiPageWikiLink Commutative.
- Hilbert_C*-module wikiPageWikiLink Commutative_property.
- Hilbert_C*-module wikiPageWikiLink Complex_conjugate.
- Hilbert_C*-module wikiPageWikiLink Complex_conjugation.
- Hilbert_C*-module wikiPageWikiLink Complex_number.
- Hilbert_C*-module wikiPageWikiLink Conjugate_linear.
- Hilbert_C*-module wikiPageWikiLink Dense_set.
- Hilbert_C*-module wikiPageWikiLink Direct_sum_of_modules.
- Hilbert_C*-module wikiPageWikiLink Euclidean_space.
- Hilbert_C*-module wikiPageWikiLink Groupoid.
- Hilbert_C*-module wikiPageWikiLink Hilbert_space.
- Hilbert_C*-module wikiPageWikiLink Induced_representation.
- Hilbert_C*-module wikiPageWikiLink Inner_product.
- Hilbert_C*-module wikiPageWikiLink Inner_product_space.
- Hilbert_C*-module wikiPageWikiLink Involution_(mathematics).
- Hilbert_C*-module wikiPageWikiLink Irving_Kaplansky.
- Hilbert_C*-module wikiPageWikiLink KK-theory.
- Hilbert_C*-module wikiPageWikiLink Locally_compact_Hausdorff_space.
- Hilbert_C*-module wikiPageWikiLink Locally_compact_space.
- Hilbert_C*-module wikiPageWikiLink Marc_Rieffel.
- Hilbert_C*-module wikiPageWikiLink Mathematical_object.
- Hilbert_C*-module wikiPageWikiLink Module_(mathematics).
- Hilbert_C*-module wikiPageWikiLink Morita_equivalence.
- Hilbert_C*-module wikiPageWikiLink Net_(mathematics).
- Hilbert_C*-module wikiPageWikiLink Noncommutative_geometry.
- Hilbert_C*-module wikiPageWikiLink Operator_algebra.
- Hilbert_C*-module wikiPageWikiLink Riemannian_manifold.
- Hilbert_C*-module wikiPageWikiLink Riemannian_metric.
- Hilbert_C*-module wikiPageWikiLink Self-adjoint.
- Hilbert_C*-module wikiPageWikiLink Sesquilinear_form.
- Hilbert_C*-module wikiPageWikiLink Spectrum_(functional_analysis).
- Hilbert_C*-module wikiPageWikiLink Unital_algebra.
- Hilbert_C*-module wikiPageWikiLink Vector_bundle.
- Hilbert_C*-module wikiPageWikiLink Vector_bundles.
- Hilbert_C*-module wikiPageWikiLink Vector_space.
- Hilbert_C*-module wikiPageWikiLinkText "Hilbert C*-module".
- Hilbert_C*-module hasPhotoCollection Hilbert_C*-module.
- Hilbert_C*-module title "Hilbert C*-Module".
- Hilbert_C*-module urlname "HilbertC-Star-Module".
- Hilbert_C*-module wikiPageUsesTemplate Template:Cite_book.
- Hilbert_C*-module wikiPageUsesTemplate Template:MathWorld.
- Hilbert_C*-module wikiPageUsesTemplate Template:Reflist.
- Hilbert_C*-module subject Category:C*-algebras.
- Hilbert_C*-module subject Category:Operator_theory.
- Hilbert_C*-module subject Category:Theoretical_physics.
- Hilbert_C*-module hypernym Objects.
- Hilbert_C*-module type Planet.
- 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 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=681363885.
- Hilbert_C*-module isPrimaryTopicOf Hilbert_C*-module.