{
  "http://en.wikipedia.org/wiki/State_(functional_analysis)" : { "http://xmlns.com/foaf/0.1/primaryTopic" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Glossary_of_functional_analysis" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Gelfand\u2013Naimark\u2013Segal_construction" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/C*-algebra" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Local_quantum_field_theory" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Choquet_theory" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/State_(functional_analysis)" : { "http://www.w3.org/2002/07/owl#sameAs" : [ { "type" : "uri", "value" : "http://rdf.freebase.com/ns/m.02bj_w" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ,
      { "type" : "uri", "value" : "http://www.wikidata.org/entity/Q2917249" } ,
      { "type" : "uri", "value" : "http://de.dbpedia.org/resource/Zustand_(Mathematik)" } ,
      { "type" : "uri", "value" : "https://global.dbpedia.org/id/2i1dp" } ,
      { "type" : "uri", "value" : "http://he.dbpedia.org/resource/\u05DE\u05E6\u05D1_(\u05D0\u05E0\u05DC\u05D9\u05D6\u05D4_\u05E4\u05D5\u05E0\u05E7\u05E6\u05D9\u05D5\u05E0\u05DC\u05D9\u05EA)" } ,
      { "type" : "uri", "value" : "http://pt.dbpedia.org/resource/Estado_(an\u00E1lise_funcional)" } ,
      { "type" : "uri", "value" : "http://ko.dbpedia.org/resource/\uC0C1\uD0DC_(\uD568\uC218\uD574\uC11D\uD559)" } ] ,
    "http://www.w3.org/2000/01/rdf-schema#label" : [ { "type" : "literal", "value" : "Estado (an\u00E1lise funcional)" , "lang" : "pt" } ,
      { "type" : "literal", "value" : "State (functional analysis)" , "lang" : "en" } ,
      { "type" : "literal", "value" : "Zustand (Mathematik)" , "lang" : "de" } ,
      { "type" : "literal", "value" : "\uC0C1\uD0DC (\uD568\uC218\uD574\uC11D\uD559)" , "lang" : "ko" } ] ,
    "http://purl.org/dc/terms/subject" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Category:C*-algebras" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Category:Functional_analysis" } ] ,
    "http://www.w3.org/ns/prov#wasDerivedFrom" : [ { "type" : "uri", "value" : "http://en.wikipedia.org/wiki/State_(functional_analysis)?oldid=1298142645&ns=0" } ] ,
    "http://xmlns.com/foaf/0.1/isPrimaryTopicOf" : [ { "type" : "uri", "value" : "http://en.wikipedia.org/wiki/State_(functional_analysis)" } ] ,
    "http://dbpedia.org/property/proof" : [ { "type" : "literal", "value" : "A proof can be sketched as follows:\nLet  be the weak*-compact set of positive linear functionals on  with norm \u2264 1, and  be the continuous functions on .\n\n can be viewed as a closed linear subspace of  . By Hahn\u2013Banach,  extends to a  in  with .\n\nUsing results from measure theory quoted above, one has:\n\n\n\nwhere, by the self-adjointness of ,  can be taken to be a signed measure. Write:\n\n\n\na difference of positive measures.\nThe restrictions of the functionals   and  to  has the required properties of  and .\nThis proves the theorem." , "lang" : "en" } ] ,
    "http://dbpedia.org/property/drop" : [ { "type" : "literal", "value" : "hidden" , "lang" : "en" } ] ,
    "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Richard_V._Kadison" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/GNS_construction" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Functional_analysis" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Net_(mathematics)" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Hahn_decomposition_theorem" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Quantum_mechanics" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Gelfand_representation" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Category:Functional_analysis" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Quantum_state" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Krein-Milman_theorem" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Operator_system" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Gelfand\u2013Naimark\u2013Segal_construction" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Operator_norm" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Positive_linear_functional" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Category:C*-algebras" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Generalization" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Choquet_theory" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Probability_measure" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Signed_measure" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/C*-algebra" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Von_Neumann_algebra" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Density_matrix" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Radon_measure" } ] ,
    "http://dbpedia.org/ontology/description" : [ { "type" : "literal", "value" : "pozitiva lineara funkcionalo de normo 1" , "lang" : "eo" } ,
      { "type" : "literal", "value" : "in functional analysis, a positive linear functional of norm 1" , "lang" : "en" } ,
      { "type" : "literal", "value" : "em an\u00E1lise funcional, um funcional linear positivo de normal 1" , "lang" : "pt" } ,
      { "type" : "literal", "value" : "mathematischer Begriff" , "lang" : "de" } ] ,
    "http://dbpedia.org/property/wikiPageUsesTemplate" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Template:Math_proof" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Template:Ordered_topological_vector_spaces" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Template:Functional_analysis" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Template:Math_theorem" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Template:Hilbert_space" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Template:Citation" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Template:Refimprove" } ] } ,
  "http://dbpedia.org/resource/Universal_representation_(C*-algebra)" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Quantum_state" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/State_variable" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Kadison\u2013Singer_problem" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Commutation_theorem_for_traces" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/State" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] ,
    "http://dbpedia.org/ontology/wikiPageDisambiguates" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Density_matrix" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Bochner's_theorem" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Tracial_state" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] ,
    "http://dbpedia.org/ontology/wikiPageRedirects" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Spectrum_of_a_C*-algebra" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Hamiltonian_mechanics" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Stinespring_dilation_theorem" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Noncommutative_torus" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Bunce\u2013Deddens_algebra" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Borchers_algebra" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Dirac\u2013von_Neumann_axioms" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Determinant" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Von_Neumann_algebra" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Noncommutative_topology" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Channel-state_duality" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] } ,
  "http://dbpedia.org/resource/Completely_positive_map" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/State_(functional_analysis)" } ] }
}