About: Jordan operator algebra

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Jordan operator algebra Goto Sponge NotDistinct Permalink

An Entity of Type : yago:Science105999797, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FJordan_operator_algebra&invfp=IFP_OFF&sas=SAME_AS_OFF

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 . 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

Attributes	Values
rdf:type	Thing yago:WikicatNon-associativeAlgebras yago:WikicatOperatorAlgebras yago:Abstraction100002137 yago:Algebra106012726 yago:Cognition100023271 yago:Content105809192 yago:Discipline105996646 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 yago:Science105999797
rdfs:label	Jordan operator algebra (en)
rdfs: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 . 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 (en)
rdfs:seeAlso	Euclidean Jordan algebra
dcterms:subject	Operator theory Functional analysis Non-associative algebras Operator algebras
Wikipage page ID	39304879 (xsd:integer)
Wikipage revision ID	1094353646 (xsd:integer)
Link from a Wikipage to another Wikipage	Quantum mechanics Quaternion C* algebra Euclidean Jordan algebra Hurwitz's theorem (composition algebras) Jordan algebra Von Neumann algebra Operator theory Complex number Mathematics Gelfand–Naimark–Segal construction Operator norm Modular lattice Lp space Complex geometry Irving Kaplansky Alain Connes Ergodic flow Kaplansky density theorem Functional analysis Advances in Mathematics Albert algebra Non-associative algebras Symmetric cone Tomita–Takesaki theory Associative algebra Operator algebras Spectral radius Octonion Real numbers Weak operator topology Ultraweak topology Max Koecher Jordan triple system Formally real Jordan algebra Bounded symmetric domain dbr:Quaternionic_Hilbert_space
Link from a Wikipage to an external page	http://www.math.ntnu.no/~hanche/joa/
sameAs	Jordan operator algebra Jordan operator algebra Jordan operator algebra Jordan operator algebra
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvtxt dbt:Reflist dbt:See_also dbt:Sfrac
has 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 . 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 *-anti-automorphism. 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. (en)
gold:hypernym	Algebras
prov:wasDerivedFrom	wikipedia-en:Jordan_operator_algebra?oldid=1094353646&ns=0
page length (characters) of wiki page	19520 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Jordan_operator_algebra
is Link from a Wikipage to another Wikipage of	Jordan algebra JBW algebra Erling Størmer Symmetric cone C-algebra JB-algebra JC-algebra Banach Jordan algebra Spin factor
is Wikipage redirect of	JBW algebra JB*-algebra JC-algebra Banach Jordan algebra Spin factor
is foaf:primaryTopic of	wikipedia-en:Jordan_operator_algebra

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 67 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software