About: Gelfand–Naimark–Segal construction

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In functional analysis, a discipline within mathematics, given a C*-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic *-representations of A and certain linear functionals on A (called states). The correspondence is shown by an explicit construction of the *-representation from the state. It is named for Israel Gelfand, Mark Naimark, and Irving Segal.

Attributes	Values
rdfs:label	Gelfand–Naimark–Segal construction (en) GNS構成法 (ja)
rdfs:comment	In functional analysis, a discipline within mathematics, given a C-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic -representations of A and certain linear functionals on A (called states). The correspondence is shown by an explicit construction of the -representation from the state. It is named for Israel Gelfand, Mark Naimark, and Irving Segal. (en) 作用素代数において、GNS構成法（GNSこうせいほう、英: GNS construction）、またはGelfand–Naimark–Segal構成法とはC-代数に状態と呼ばれる線形汎関数が与えられたときに、巡回表現と呼ばれる特別な表現を構成する方法。GNSの語は考案者である3人の数学者Gelfand、Naimark、Segalの頭文字に由来する。場の量子論や量子統計力学では、ヒルベルト空間を離れ、物理量のなす代数のみから理論を構築してもGNS構成法により、全ての物理量の期待値が与えられたときに、逆にヒルベルト空間とその上の作用による物理量の表現を構成することができる。自由度が無限大である系では、当初に設定した空間を飛び出さねばならないことが多い。このときGNS構成法を用いれば、新しいヒルベルト空間を作ることができる。 (ja)
dcterms:subject	Axiomatic quantum field theory C*-algebras Functional analysis
Wikipage page ID	297446 (xsd:integer)
Wikipage revision ID	1119527001 (xsd:integer)
Link from a Wikipage to another Wikipage	Enveloping von Neumann algebra Nondegenerate Axiomatic quantum field theory John von Neumann Riesz–Markov–Kakutani representation theorem Cyclic and separating vector Positive linear functional Convex set Mathematics Gelfand–Naimark theorem Gennadi Sardanashvily Bounded operator Approximate identity State (functional analysis) Stinespring factorization theorem Completely positive map Functional analysis William Arveson Banach–Alaoglu theorem Adjoint Cauchy completion Irreducible representation Extreme point Faithful functor Deformation quantization Linear functional Quotient space (linear algebra) Hilbert space Involution (mathematics) Irving Segal Israel Gelfand Jacques Dixmier C-algebras Functional analysis Mark Naimark C-algebra Krein–Milman theorem Radon–Nikodym theorem Map (mathematics) Weak operator topology Universal representation (C*-algebra) Sesquilinear form Ring homomorphism B-star algebra Kadison, Richard Left ideal Commutant dbr:KSGNS_construction
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=S8sZiieo-04C&pg=PA371 https://books.google.com/books%3Fid=xuq8CHNEFKoC&pg=PA113
sameAs	Gelfand–Naimark–Segal construction Gelfand–Naimark–Segal construction Gelfand–Naimark–Segal construction Gelfand–Naimark–Segal construction Gelfand–Naimark–Segal construction
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:ISBN dbt:Reflist dbt:Short_description
Link from a Wikipa... related subject.	dbpedia-ru:Алгебраическая_квантовая_теория
has abstract	In functional analysis, a discipline within mathematics, given a C-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic -representations of A and certain linear functionals on A (called states). The correspondence is shown by an explicit construction of the -representation from the state. It is named for Israel Gelfand, Mark Naimark, and Irving Segal. (en) 作用素代数において、GNS構成法（GNSこうせいほう、英: GNS construction）、またはGelfand–Naimark–Segal構成法とはC-代数に状態と呼ばれる線形汎関数が与えられたときに、巡回表現と呼ばれる特別な表現を構成する方法。GNSの語は考案者である3人の数学者Gelfand、Naimark、Segalの頭文字に由来する。場の量子論や量子統計力学では、ヒルベルト空間を離れ、物理量のなす代数のみから理論を構築してもGNS構成法により、全ての物理量の期待値が与えられたときに、逆にヒルベルト空間とその上の作用による物理量の表現を構成することができる。自由度が無限大である系では、当初に設定した空間を飛び出さねばならないことが多い。このときGNS構成法を用いれば、新しいヒルベルト空間を作ることができる。 (ja)
prov:wasDerivedFrom	wikipedia-en:Gelfand–Naimark–Segal_construction?oldid=1119527001&ns=0
page length (characters) of wiki page	13521 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Gelfand–Naimark–Segal_construction
is Link from a Wikipage to another Wikipage of	Quantum state List of functional analysis topics Bra–ket notation Cyclic and separating vector Von Neumann algebra GNS -representation Gelfand Naimark State (functional analysis) Zonal spherical function Representation theorem Jordan operator algebra List of algebraic constructions Irving Segal Israel Gelfand Tomita–Takesaki theory Mark Naimark C-algebra Inner product space Gelfand-Naimark-Segal construction Segal Siegel Universal representation (C*-algebra) Stinespring dilation theorem GNS construction

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