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- C*-algebra abstract "C∗-algebras (pronounced "C-star") are an important area of research in functional analysis, a branch of mathematics. A C*-algebra is a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: A is a topologically closed set in the norm topology of operators. A is closed under the operation of taking adjoints of operators.C*-algebras were first considered primarily for their use in quantum mechanics to model algebras of physical observables. This line of research began with Werner Heisenberg's matrix mechanics and in a more mathematically developed form with Pascual Jordan around 1933. Subsequently John von Neumann attempted to establish a general framework for these algebras which culminated in a series of papers on rings of operators. These papers considered a special class of C*-algebras which are now known as von Neumann algebras.Around 1943, the work of Israel Gelfand and Mark Naimark yielded an abstract characterisation of C*-algebras making no reference to operators on a Hilbert space.C*-algebras are now an important tool in the theory of unitary representations of locally compact groups, and are also used in algebraic formulations of quantum mechanics. Another active area of research is the program to obtain classification, or to determine the extent of which classification is possible, for separable simple nuclear C*-algebras.".
- C*-algebra wikiPageID "7184".
- C*-algebra wikiPageLength "18238".
- C*-algebra wikiPageOutDegree "102".
- C*-algebra wikiPageRevisionID "678423647".
- C*-algebra wikiPageWikiLink *-algebra.
- C*-algebra wikiPageWikiLink Adjoint_of_an_operator.
- C*-algebra wikiPageWikiLink Adjoint_operator.
- C*-algebra wikiPageWikiLink Algebra_over_a_field.
- C*-algebra wikiPageWikiLink Approximate_identity.
- C*-algebra wikiPageWikiLink Approximately_finite-dimensional_C*-algebra.
- C*-algebra wikiPageWikiLink Approximately_finite_dimensional_C*-algebra.
- C*-algebra wikiPageWikiLink Artin–Wedderburn_theorem.
- C*-algebra wikiPageWikiLink Banach_*-algebra.
- C*-algebra wikiPageWikiLink Banach_algebra.
- C*-algebra wikiPageWikiLink Bounded_linear_map.
- C*-algebra wikiPageWikiLink Bounded_operator.
- C*-algebra wikiPageWikiLink Calkin_algebra.
- C*-algebra wikiPageWikiLink Canonical_form.
- C*-algebra wikiPageWikiLink Category:C*-algebras.
- C*-algebra wikiPageWikiLink Category:Theoretical_physics.
- C*-algebra wikiPageWikiLink Character_(mathematics).
- C*-algebra wikiPageWikiLink Closed_set.
- C*-algebra wikiPageWikiLink Compact_operator_on_Hilbert_space.
- C*-algebra wikiPageWikiLink Complex_number.
- C*-algebra wikiPageWikiLink Conceptual_model.
- C*-algebra wikiPageWikiLink Conjugate_transpose.
- C*-algebra wikiPageWikiLink Continuous_functional_calculus.
- C*-algebra wikiPageWikiLink Continuous_linear_operator.
- C*-algebra wikiPageWikiLink Convex_cone.
- C*-algebra wikiPageWikiLink Direct_sum_of_modules.
- C*-algebra wikiPageWikiLink Functional_analysis.
- C*-algebra wikiPageWikiLink GNS_construction.
- C*-algebra wikiPageWikiLink Gelfand_isomorphism.
- C*-algebra wikiPageWikiLink Gelfand_representation.
- C*-algebra wikiPageWikiLink Gelfand–Naimark_theorem.
- C*-algebra wikiPageWikiLink Gelfand–Naimark–Segal_construction.
- C*-algebra wikiPageWikiLink Group_C%5E*-algebra.
- C*-algebra wikiPageWikiLink Group_algebra.
- C*-algebra wikiPageWikiLink Harmonic_analysis.
- C*-algebra wikiPageWikiLink Hereditary_C*-subalgebra.
- C*-algebra wikiPageWikiLink Hermitian_adjoint.
- C*-algebra wikiPageWikiLink Hilbert_C*-module.
- C*-algebra wikiPageWikiLink Hilbert_space.
- C*-algebra wikiPageWikiLink Homeomorphism.
- C*-algebra wikiPageWikiLink Ideal_(ring_theory).
- C*-algebra wikiPageWikiLink Irving_Segal.
- C*-algebra wikiPageWikiLink Isometry.
- C*-algebra wikiPageWikiLink Isomorphism.
- C*-algebra wikiPageWikiLink Israel_Gelfand.
- C*-algebra wikiPageWikiLink James_Glimm.
- C*-algebra wikiPageWikiLink John_von_Neumann.
- C*-algebra wikiPageWikiLink Linear_map.
- C*-algebra wikiPageWikiLink Linear_operator.
- C*-algebra wikiPageWikiLink Local_quantum_field_theory.
- C*-algebra wikiPageWikiLink Locally_compact.
- C*-algebra wikiPageWikiLink Locally_compact_group.
- C*-algebra wikiPageWikiLink Locally_compact_space.
- C*-algebra wikiPageWikiLink Map_(mathematics).
- C*-algebra wikiPageWikiLink Mark_Naimark.
- C*-algebra wikiPageWikiLink Mathematics.
- C*-algebra wikiPageWikiLink Matrix_(mathematics).
- C*-algebra wikiPageWikiLink Matrix_mechanics.
- C*-algebra wikiPageWikiLink Metric_map.
- C*-algebra wikiPageWikiLink Minkowski_space.
- C*-algebra wikiPageWikiLink Minkowski_spacetime.
- C*-algebra wikiPageWikiLink Model_(abstract).
- C*-algebra wikiPageWikiLink Noncommutative_geometry.
- C*-algebra wikiPageWikiLink Noncommutative_topology.
- C*-algebra wikiPageWikiLink Norm_closed.
- C*-algebra wikiPageWikiLink Norm_topology.
- C*-algebra wikiPageWikiLink Nuclear_C*-algebra.
- C*-algebra wikiPageWikiLink Observable.
- C*-algebra wikiPageWikiLink Operator_K-theory.
- C*-algebra wikiPageWikiLink Operator_norm.
- C*-algebra wikiPageWikiLink Operator_system.
- C*-algebra wikiPageWikiLink Ordered_group.
- C*-algebra wikiPageWikiLink Partial_order.
- C*-algebra wikiPageWikiLink Partially_ordered_group.
- C*-algebra wikiPageWikiLink Partially_ordered_set.
- C*-algebra wikiPageWikiLink Pascual_Jordan.
- C*-algebra wikiPageWikiLink Positive_linear_functional.
- C*-algebra wikiPageWikiLink Quantum_mechanics.
- C*-algebra wikiPageWikiLink Quotient.
- C*-algebra wikiPageWikiLink Semigroup_with_involution.
- C*-algebra wikiPageWikiLink Semisimple_algebra.
- C*-algebra wikiPageWikiLink Separable_space.
- C*-algebra wikiPageWikiLink Sherman–Takeda_theorem.
- C*-algebra wikiPageWikiLink Short_map.
- C*-algebra wikiPageWikiLink Spectral_radius.
- C*-algebra wikiPageWikiLink Spectrum_(functional_analysis).
- C*-algebra wikiPageWikiLink Spectrum_of_a_C*-algebra.
- C*-algebra wikiPageWikiLink Star-algebra.
- C*-algebra wikiPageWikiLink State_(functional_analysis).
- C*-algebra wikiPageWikiLink Tietze_extension_theorem.
- C*-algebra wikiPageWikiLink Unitary_representation.
- C*-algebra wikiPageWikiLink Universal_morphism.
- C*-algebra wikiPageWikiLink Universal_property.
- C*-algebra wikiPageWikiLink Vector_space.
- C*-algebra wikiPageWikiLink Von_Neumann_algebra.