{"id":"https://openalex.org/W2145003579","doi":"https://doi.org/10.1142/s0219025700000261","title":"TENSOR PRODUCT SYSTEMS OF HILBERT MODULES AND DILATIONS OF COMPLETELY POSITIVE SEMIGROUPS","display_name":"TENSOR PRODUCT SYSTEMS OF HILBERT MODULES AND DILATIONS OF COMPLETELY POSITIVE SEMIGROUPS","publication_year":2000,"publication_date":"2000-12-01","ids":{"openalex":"https://openalex.org/W2145003579","doi":"https://doi.org/10.1142/s0219025700000261","mag":"2145003579"},"language":"en","primary_location":{"id":"doi:10.1142/s0219025700000261","doi":"https://doi.org/10.1142/s0219025700000261","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219025700000261","pdf_url":null,"source":{"id":"https://openalex.org/S207478012","display_name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","issn_l":"0219-0257","issn":["0219-0257","1793-6306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-2","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Infinite Dimensional Analysis, Quantum Probability and Related Topics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"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/A5049792750","display_name":"B. V. Rajarama Bhat","orcid":"https://orcid.org/0000-0002-4614-8890","observed_orcids":["https://orcid.org/0000-0002-4614-8890"]},"institutions":[{"id":"https://openalex.org/I4405280447","display_name":"Indian Statistical Institute, Bangalore Centre","ror":"https://ror.org/02yqprq16","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405280447","https://openalex.org/I6498739"]},{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"B. V. RAJARAMA BHAT","raw_affiliation_strings":["Statistics and Mathematics Unit, Indian Statistical Institute, R. V. College Post, Bangalore 560059, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Statistics and Mathematics Unit, Indian Statistical Institute, R. V. College Post, Bangalore 560059, India","institution_ids":["https://openalex.org/I4405280447","https://openalex.org/I6498739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000933051","display_name":"Michael Skeide","orcid":"https://orcid.org/0000-0002-6183-1022","observed_orcids":["https://orcid.org/0000-0002-6183-1022"]},"institutions":[{"id":"https://openalex.org/I51783024","display_name":"Brandenburg University of Technology Cottbus-Senftenberg","ror":"https://ror.org/02wxx3e24","country_code":"DE","type":"education","lineage":["https://openalex.org/I51783024"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"MICHAEL SKEIDE","raw_affiliation_strings":["Lehrstuhl f\u00fcr Wahrscheinlichkeitstheorie und Statistik, Brandenburgische Technische Universit\u00e4t Cottbus, Postfach 101344, D-03013 Cottbus, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehrstuhl f\u00fcr Wahrscheinlichkeitstheorie und Statistik, Brandenburgische Technische Universit\u00e4t Cottbus, Postfach 101344, D-03013 Cottbus, Germany","institution_ids":["https://openalex.org/I51783024"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.2101,"has_fulltext":false,"cited_by_count":112,"citation_normalized_percentile":{"value":0.99020979,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"03","issue":"04","first_page":"519","last_page":"575"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9984999895095825,"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":0.9984999895095825,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dilation-theory","display_name":"dilation theory","score":0.828000009059906},{"id":"https://openalex.org/keywords/e0-semigroups","display_name":"E0-semigroups","score":0.8220000267028809},{"id":"https://openalex.org/keywords/product-systems","display_name":"product systems","score":0.5979999899864197},{"id":"https://openalex.org/keywords/quantum-dynamical-semigroups","display_name":"quantum dynamical semigroups","score":0.8539999723434448},{"id":"https://openalex.org/keywords/cocycle-conjugacy","display_name":"cocycle conjugacy","score":0.9409999847412109},{"id":"https://openalex.org/keywords/adjointable-operators","display_name":"adjointable operators","score":0.6370000243186951},{"id":"https://openalex.org/keywords/c-algebras","display_name":"C*-algebras","score":0.7760000228881836}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8152453899383545},{"id":"https://openalex.org/C116858840","wikidata":"https://www.wikidata.org/wiki/Q1340800","display_name":"Endomorphism","level":2,"score":0.7800830602645874},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6756327152252197},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6637779474258423},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6576221585273743},{"id":"https://openalex.org/C46149467","wikidata":"https://www.wikidata.org/wiki/Q7574800","display_name":"Special classes of semigroups","level":3,"score":0.6113300919532776},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.5727295279502869},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5272979736328125},{"id":"https://openalex.org/C30397308","wikidata":"https://www.wikidata.org/wiki/Q6438788","display_name":"Krohn\u2013Rhodes theory","level":4,"score":0.5030316710472107},{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.44604814052581787},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40523380041122437},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3688986897468567},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1576717495918274}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0219025700000261","doi":"https://doi.org/10.1142/s0219025700000261","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219025700000261","pdf_url":null,"source":{"id":"https://openalex.org/S207478012","display_name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","issn_l":"0219-0257","issn":["0219-0257","1793-6306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-2","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Infinite Dimensional Analysis, Quantum Probability and Related Topics","raw_type":"journal-article"},{"id":"pmh:oai:iris.unimol.it:11695/7000","doi":null,"is_oa":false,"landing_page_url":"https://hdl.handle.net/11695/7000","pdf_url":null,"source":{"id":"https://openalex.org/S7407055127","display_name":"Archivio Istituzionale della Ricerca - Universit\u00e0 degli Studi del Molise","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1524878283","https://openalex.org/W1544022757","https://openalex.org/W1608564739","https://openalex.org/W1882874209","https://openalex.org/W1971896797","https://openalex.org/W1974335160","https://openalex.org/W1978199434","https://openalex.org/W1992235689","https://openalex.org/W1998010282","https://openalex.org/W2002490441","https://openalex.org/W2005367585","https://openalex.org/W2018746720","https://openalex.org/W2021334407","https://openalex.org/W2021597056","https://openalex.org/W2028749341","https://openalex.org/W2033285702","https://openalex.org/W2052771093","https://openalex.org/W2054035194","https://openalex.org/W2072417354","https://openalex.org/W2072443384","https://openalex.org/W2084265277","https://openalex.org/W2121426613","https://openalex.org/W2166827810","https://openalex.org/W2331274486","https://openalex.org/W2395780602","https://openalex.org/W3000705579","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W7217301853","https://openalex.org/W7062358730","https://openalex.org/W7095555815","https://openalex.org/W2049559069","https://openalex.org/W2937653962","https://openalex.org/W155438400","https://openalex.org/W7099612833","https://openalex.org/W2017489896","https://openalex.org/W2962762155","https://openalex.org/W7100487657"],"abstract_inverted_index":{"In":[0,44,87],"this":[1,45],"paper":[2],"we":[3,47,93],"study":[4],"the":[5,29,52,68,88,117,173,200],"problem":[6],"of":[7,25,31,70,74,90,105,141,162,203,215],"dilating":[8],"unital":[9,151],"completely":[10],"positive":[11],"(CP)":[12],"semigroups":[13,24,109],"(quantum":[14],"dynamical":[15],"semigroups)":[16],"to":[17,23,42,50,61,67,98,120,135,156],"weak":[18],"Markov":[19],"flows":[20],"and":[21,77,102],"then":[22],"endomorphisms":[26,60],"(E0-semigroups)":[27],"using":[28],"language":[30],"Hilbert":[32,75,85,142,163,208],"modules.":[33,164],"This":[34],"is":[35,191],"a":[36,207],"very":[37],"effective,":[38],"representation":[39],"free":[40],"approach":[41],"dilation.":[43],"way":[46],"are":[48,64,94,153],"able":[49,97],"identify":[51],"right":[53],"algebra":[54,202],"(maximal":[55],"in":[56,182],"some":[57],"sense)":[58],"for":[59,79,84,108,185,221],"act.":[62],"We":[63,144,211],"led":[65],"inevitably":[66],"notion":[69],"tensor":[71],"product":[72,139,160],"systems":[73,140,161],"modules":[76],"units":[78],"them,":[80],"generalizing":[81],"Arveson's":[82],"notions":[83],"spaces.":[86],"course":[89],"our":[91],"investigations":[92],"not":[95],"only":[96],"give":[99],"new":[100],"natural":[101],"transparent":[103],"proofs":[104],"well-known":[106],"facts":[107],"on":[110,130,149,178,187,196,206],"[Formula:":[111,131,179,188,197],"see":[112,132,180,189,198],"text],":[113,199],"but":[114],"also":[115],"extend":[116],"results":[118,217],"immediately":[119],"much":[121],"more":[122],"general":[123],"setups.":[124],"For":[125],"instance,":[126],"Arveson":[127],"classifies":[128],"E0-semigroups":[129,177,195],"text]":[133,181,190],"up":[134,155],"cocycle":[136,157],"conjugacy":[137,158],"by":[138,159,176,194,219],"spaces.5":[143],"find":[145],"that":[146,172],"conservative":[147],"CP-semigroups":[148,186],"arbitrary":[150],"C*-algebras":[152],"classified":[154],"Looking":[165],"at":[166],"other":[167],"generalizations,":[168],"it":[169],"turns":[170],"out":[171],"role":[174],"played":[175,193],"dilation":[183],"theory":[184],"now":[192],"full":[201],"adjointable":[204],"operators":[205],"module":[209],"E.":[210],"have":[212],"CP-semigroup":[213],"versions":[214],"many":[216],"proved":[218],"Paschke27":[220],"CP":[222],"maps.":[223]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}