{"id":"https://openalex.org/W4866391","doi":null,"title":"John von Neumann and the Theory of Operator Algebras","display_name":"John von Neumann and the Theory of Operator Algebras","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W4866391","mag":"4866391"},"language":"en","primary_location":{"id":"mag:4866391","doi":null,"is_oa":false,"landing_page_url":"http://math.bme.hu/~petz/2vn.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108501807","display_name":"D\u0117nes Petz","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"D\u0117nes Petz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5108501807"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.00039968,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.0015999999595806003,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.00139999995008111,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/john-von-neumann","display_name":"John von Neumann","score":0.9940000176429749},{"id":"https://openalex.org/keywords/von-neumann-algebras","display_name":"von Neumann algebras","score":0.953000009059906},{"id":"https://openalex.org/keywords/operator-algebras","display_name":"operator algebras","score":0.8970000147819519},{"id":"https://openalex.org/keywords/history-of-mathematics","display_name":"history of mathematics","score":0.7599999904632568},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"quantum mechanics","score":0.5389999747276306},{"id":"https://openalex.org/keywords/hilbert-space-operators","display_name":"Hilbert space operators","score":0.8889999985694885},{"id":"https://openalex.org/keywords/quantum-statistical-mechanics","display_name":"quantum statistical mechanics","score":0.9639999866485596},{"id":"https://openalex.org/keywords/quantum-field-theory","display_name":"quantum field theory","score":0.9610000252723694}],"concepts":[{"id":"https://openalex.org/C21261745","wikidata":"https://www.wikidata.org/wiki/Q7941491","display_name":"Von Neumann's theorem","level":4,"score":0.789695143699646},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.7818688154220581},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.7282446622848511},{"id":"https://openalex.org/C153408630","wikidata":"https://www.wikidata.org/wiki/Q1970172","display_name":"Von Neumann algebra","level":3,"score":0.6846827268600464},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6065776348114014},{"id":"https://openalex.org/C138081561","wikidata":"https://www.wikidata.org/wiki/Q4688920","display_name":"Affiliated operator","level":5,"score":0.5793139338493347},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5679218769073486},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5485287308692932},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.5226811766624451},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.5016570091247559},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4690825045108795},{"id":"https://openalex.org/C70120467","wikidata":"https://www.wikidata.org/wiki/Q515893","display_name":"Free probability","level":2,"score":0.4451260268688202},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4425809681415558},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.4370577335357666},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.42067164182662964},{"id":"https://openalex.org/C200717178","wikidata":"https://www.wikidata.org/wiki/Q606855","display_name":"Mathematical formulation of quantum mechanics","level":5,"score":0.4143044352531433},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.26375460624694824},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2314591407775879},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2226862609386444},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1774245798587799},{"id":"https://openalex.org/C82916341","wikidata":"https://www.wikidata.org/wiki/Q6934990","display_name":"Multiplication operator","level":3,"score":0.12362739443778992},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.11716380715370178},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.11544248461723328},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:4866391","doi":null,"is_oa":false,"landing_page_url":"http://math.bme.hu/~petz/2vn.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W185318156","https://openalex.org/W659231075","https://openalex.org/W1523099013","https://openalex.org/W1606975474","https://openalex.org/W1967300267","https://openalex.org/W1994275197","https://openalex.org/W2015411876","https://openalex.org/W2044063783","https://openalex.org/W2070217890","https://openalex.org/W2088529531","https://openalex.org/W2141388219","https://openalex.org/W2145952093","https://openalex.org/W2318908986","https://openalex.org/W2331578546","https://openalex.org/W2492395901","https://openalex.org/W2503907534","https://openalex.org/W2561954461"],"related_works":["https://openalex.org/W7095098959","https://openalex.org/W4239835226","https://openalex.org/W2979689202","https://openalex.org/W1524878283","https://openalex.org/W2034264245","https://openalex.org/W4244651418","https://openalex.org/W1992713445","https://openalex.org/W2312350341","https://openalex.org/W4254870475","https://openalex.org/W1894480176"],"abstract_inverted_index":{"After":[0,108],"some":[1],"earlier":[2],"work":[3],"on":[4],"single":[5],"operators,":[6],"von":[7,28,73],"Neumann":[8,29],"turned":[9],"to":[10,87,102],"families":[11],"of":[12,20,22,39,61,92,97,104,110,123],"operators":[13,23],"in":[14,45,72,84],"[1].":[15],"He":[16],"initiated":[17],"the":[18,36,58,98,116],"study":[19],"rings":[21],"which":[24,34],"are":[25],"commonly":[26],"called":[27],"algebras":[30,103],"today.":[31],"The":[32,89],"papers":[33],"constitute":[35],"series":[37],"\u201cRings":[38],"operators\u201d":[40],"opened":[41],"a":[42,52],"new":[43],"field":[44,129],"mathematics":[46],"and":[47,67,127],"influenced":[48],"research":[49],"for":[50],"half":[51],"century":[53],"(or":[54],"even":[55],"longer).":[56],"In":[57],"standard":[59],"theory":[60,81,94,119],"modern":[62],"operator":[63,79,117],"algebras,":[64],"many":[65],"concepts":[66],"ideas":[68],"have":[69],"their":[70],"origin":[71],"Neumann\u2019s":[74],"work.":[75],"Since":[76],"its":[77],"inception,":[78],"algebra":[80,118],"has":[82],"been":[83],"intimate":[85],"relation":[86],"physics.":[88],"mathematical":[90,121],"formalism":[91],"quantum":[93,124,128],"was":[95],"one":[96],"motivations":[99],"leading":[100],"naturally":[101],"Hilbert":[105],"space":[106],"operators.":[107],"decades":[109],"relative":[111],"isolation,":[112],"again":[113],"physics":[114],"fertilized":[115],"by":[120],"questions":[122],"statistical":[125],"mechanics":[126],"theory.":[130]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}