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- Jordan_operator_algebra abstract "In mathematics, Jordan operator algebras are real or complex Jordan algebras with the compatible structure of a Banach space. When the coefficients are real numbers, the algebras are called Jordan Banach algebras. The theory has been extensively developed only for the subclass of JB algebras. The axioms for these algebras were devised by Alfsen, Schultz & Størmer (1978). Those that can be realised concretely as subalgebras of self-adjoint operators on a real or complex Hilbert space with the operator Jordan product and the operator norm are called JC algebras. The axioms for complex Jordan operator algebras, first suggested by Irving Kaplansky in 1976, require an involution and are called JB* algebras or Jordan C* algebras. By analogy with the abstract characterisation of von Neumann algebras as C* algebras for which the underlying Banach space is the dual of another, there is a corresponding definition of JBW algebras. Those that can be realised using ultraweakly closed Jordan algebras of self-adjoint operators with the operator Jordan product are called JW algebras. The JBW algebras with trivial center, so-called JBW factors, are classified in terms of von Neumann factors: apart from the exceptional 27 dimensional Albert algebra and the spin factors, all other JBW factors are isomorphic either to the self-adjoint part of a von Neumann factor or to its fixed point algebra under a period two *-antiautomorphism. Jordan operator algebras have been applied in quantum mechanics and in complex geometry, where Koecher's description of bounded symmetric domains using Jordan algebras has been extended to infinite dimensions.".
- Jordan_operator_algebra wikiPageExternalLink joa.
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- Jordan_operator_algebra wikiPageID "39304879".
- Jordan_operator_algebra wikiPageLength "18579".
- Jordan_operator_algebra wikiPageOutDegree "46".
- Jordan_operator_algebra wikiPageRevisionID "663857744".
- Jordan_operator_algebra wikiPageWikiLink Alain_Connes.
- Jordan_operator_algebra wikiPageWikiLink Albert_algebra.
- Jordan_operator_algebra wikiPageWikiLink Associative_algebra.
- Jordan_operator_algebra wikiPageWikiLink Bounded_symmetric_domain.
- Jordan_operator_algebra wikiPageWikiLink C*-algebra.
- Jordan_operator_algebra wikiPageWikiLink C*_algebra.
- Jordan_operator_algebra wikiPageWikiLink Category:Functional_analysis.
- Jordan_operator_algebra wikiPageWikiLink Category:Non-associative_algebras.
- Jordan_operator_algebra wikiPageWikiLink Category:Operator_algebras.
- Jordan_operator_algebra wikiPageWikiLink Category:Operator_theory.
- Jordan_operator_algebra wikiPageWikiLink Complex_geometry.
- Jordan_operator_algebra wikiPageWikiLink Complex_number.
- Jordan_operator_algebra wikiPageWikiLink Ergodic_flow.
- Jordan_operator_algebra wikiPageWikiLink Ergodic_theory.
- Jordan_operator_algebra wikiPageWikiLink Euclidean_Jordan_algebra.
- Jordan_operator_algebra wikiPageWikiLink Formally_real_Jordan_algebra.
- Jordan_operator_algebra wikiPageWikiLink Gelfand–Naimark–Segal_construction.
- Jordan_operator_algebra wikiPageWikiLink Hermitian_symmetric_space.
- Jordan_operator_algebra wikiPageWikiLink Hurwitzs_theorem_(composition_algebras).
- Jordan_operator_algebra wikiPageWikiLink Irving_Kaplansky.
- Jordan_operator_algebra wikiPageWikiLink Jordan_algebra.
- Jordan_operator_algebra wikiPageWikiLink Jordan_triple_system.
- Jordan_operator_algebra wikiPageWikiLink Kaplansky_density_theorem.
- Jordan_operator_algebra wikiPageWikiLink Lp_space.
- Jordan_operator_algebra wikiPageWikiLink Mathematics.
- Jordan_operator_algebra wikiPageWikiLink Max_Koecher.
- Jordan_operator_algebra wikiPageWikiLink Modular_lattice.
- Jordan_operator_algebra wikiPageWikiLink Octonion.
- Jordan_operator_algebra wikiPageWikiLink Operator_norm.
- Jordan_operator_algebra wikiPageWikiLink Quantum_mechanics.
- Jordan_operator_algebra wikiPageWikiLink Quaternion.
- Jordan_operator_algebra wikiPageWikiLink Real_number.
- Jordan_operator_algebra wikiPageWikiLink Real_numbers.
- Jordan_operator_algebra wikiPageWikiLink Spectral_radius.
- Jordan_operator_algebra wikiPageWikiLink Symmetric_cone.
- Jordan_operator_algebra wikiPageWikiLink Tomita–Takesaki_theory.
- Jordan_operator_algebra wikiPageWikiLink Triple_system.
- Jordan_operator_algebra wikiPageWikiLink Ultraweak_topology.
- Jordan_operator_algebra wikiPageWikiLink Von_Neumann_algebra.
- Jordan_operator_algebra wikiPageWikiLink Weak_operator_topology.
- Jordan_operator_algebra wikiPageWikiLinkText "'''Jordan C* algebra'''".
- Jordan_operator_algebra wikiPageWikiLinkText "Jordan operator algebra".
- Jordan_operator_algebra hasPhotoCollection Jordan_operator_algebra.
- Jordan_operator_algebra wikiPageUsesTemplate Template:Citation.
- Jordan_operator_algebra wikiPageUsesTemplate Template:Harvtxt.
- Jordan_operator_algebra wikiPageUsesTemplate Template:Reflist.
- Jordan_operator_algebra wikiPageUsesTemplate Template:Seealso.
- Jordan_operator_algebra subject Category:Functional_analysis.
- Jordan_operator_algebra subject Category:Non-associative_algebras.
- Jordan_operator_algebra subject Category:Operator_algebras.
- Jordan_operator_algebra subject Category:Operator_theory.
- Jordan_operator_algebra hypernym Algebras.
- Jordan_operator_algebra type Algebra.
- Jordan_operator_algebra type Function.
- Jordan_operator_algebra type Physic.
- Jordan_operator_algebra type Thing.
- Jordan_operator_algebra comment "In mathematics, Jordan operator algebras are real or complex Jordan algebras with the compatible structure of a Banach space. When the coefficients are real numbers, the algebras are called Jordan Banach algebras. The theory has been extensively developed only for the subclass of JB algebras. The axioms for these algebras were devised by Alfsen, Schultz & Størmer (1978).".
- Jordan_operator_algebra label "Jordan operator algebra".
- Jordan_operator_algebra seeAlso Symmetric_cone.
- Jordan_operator_algebra sameAs m.0v3f3zm.
- Jordan_operator_algebra sameAs Q17098325.
- Jordan_operator_algebra sameAs Q17098325.
- Jordan_operator_algebra wasDerivedFrom Jordan_operator_algebra?oldid=663857744.
- Jordan_operator_algebra isPrimaryTopicOf Jordan_operator_algebra.