Algebra of operators affiliated with a finite type I von Neumann algebra

Name: Work Video:
Duration: 3 min 30 s
Description: It is shown that the *-algebra of all (closed densely defined linear) operators affiliated with a finite type I von Neumann algebra admits a unique center-valued trace, which turns out to be, in a sense, normal. It is also demonstrated that for no other von Neumann algebras similar constructions can be performed.
Piotr Niemiec; Adam Wegert
{'id': 'https://openalex.org/W1511064543', 'doi': None, 'title': 'Algebra of operators affiliated with a finite type I von Neumann algebra', 'display_name': 'Algebra of operators affiliated with a finite type I von Neumann algebra', 'publication_year': 2013, 'publication_date': '2013-07-17', 'ids': {'openalex': 'https://openalex.org/W1511064543', 'mag': '1511064543'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://arxiv.org/pdf/1307.4696', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_indexed_in_scopus': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'type': 'preprint', 'type_crossref': 'posted-content', 'indexed_in': [], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5011006691', 'display_name': 'Piotr Niemiec', 'orcid': 'https://orcid.org/0000-0003-2393-8299'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Piotr Niemiec', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5046446370', 'display_name': 'Adam Wegert', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Adam Wegert', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 1, 'citation_normalized_percentile': {'value': 0.593273, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 65, 'max': 72}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10899', 'display_name': 'Advanced Operator Algebra Research', 'score': 1.0, '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': 1.0, '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/T11673', 'display_name': 'Advanced Topics in Algebra', 'score': 0.9994, 'subfield': {'id': 'https://openalex.org/subfields/2602', 'display_name': 'Algebra and Number Theory'}, '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/T11022', 'display_name': 'Spectral Theory in Mathematical Physics', 'score': 0.998, '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/von-neumann-algebra', 'display_name': 'Von Neumann algebra', 'score': 0.92331374}, {'id': 'https://openalex.org/keywords/affiliated-operator', 'display_name': 'Affiliated operator', 'score': 0.86177504}, {'id': 'https://openalex.org/keywords/trace', 'display_name': 'TRACE (psycholinguistics)', 'score': 0.6384697}, {'id': 'https://openalex.org/keywords/center', 'display_name': 'Center (category theory)', 'score': 0.5031068}, {'id': 'https://openalex.org/keywords/tomita–takesaki-theory', 'display_name': 'Tomita–Takesaki theory', 'score': 0.49877024}], 'concepts': [{'id': 'https://openalex.org/C153408630', 'wikidata': 'https://www.wikidata.org/wiki/Q1970172', 'display_name': 'Von Neumann algebra', 'level': 3, 'score': 0.92331374}, {'id': 'https://openalex.org/C138081561', 'wikidata': 'https://www.wikidata.org/wiki/Q4688920', 'display_name': 'Affiliated operator', 'level': 5, 'score': 0.86177504}, {'id': 'https://openalex.org/C144133476', 'wikidata': 'https://www.wikidata.org/wiki/Q4666687', 'display_name': 'Abelian von Neumann algebra', 'level': 5, 'score': 0.834497}, {'id': 'https://openalex.org/C75291252', 'wikidata': 'https://www.wikidata.org/wiki/Q1315756', 'display_name': 'TRACE (psycholinguistics)', 'level': 2, 'score': 0.6384697}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.6356643}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.61500365}, {'id': 'https://openalex.org/C100376341', 'wikidata': 'https://www.wikidata.org/wiki/Q649977', 'display_name': 'Jordan algebra', 'level': 4, 'score': 0.55696}, {'id': 'https://openalex.org/C80469333', 'wikidata': 'https://www.wikidata.org/wiki/Q189088', 'display_name': 'Von Neumann architecture', 'level': 2, 'score': 0.53811294}, {'id': 'https://openalex.org/C21261745', 'wikidata': 'https://www.wikidata.org/wiki/Q7941491', 'display_name': "Von Neumann's theorem", 'level': 4, 'score': 0.5325626}, {'id': 'https://openalex.org/C2777299769', 'wikidata': 'https://www.wikidata.org/wiki/Q3707858', 'display_name': 'Type (biology)', 'level': 2, 'score': 0.5039293}, {'id': 'https://openalex.org/C2779463800', 'wikidata': 'https://www.wikidata.org/wiki/Q5062222', 'display_name': 'Center (category theory)', 'level': 2, 'score': 0.5031068}, {'id': 'https://openalex.org/C54512446', 'wikidata': 'https://www.wikidata.org/wiki/Q7818977', 'display_name': 'Tomita–Takesaki theory', 'level': 5, 'score': 0.49877024}, {'id': 'https://openalex.org/C169171071', 'wikidata': 'https://www.wikidata.org/wiki/Q5449241', 'display_name': 'Filtered algebra', 'level': 3, 'score': 0.4954599}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.47870234}, {'id': 'https://openalex.org/C100899422', 'wikidata': 'https://www.wikidata.org/wiki/Q5058347', 'display_name': 'Cellular algebra', 'level': 4, 'score': 0.45656782}, {'id': 'https://openalex.org/C14394260', 'wikidata': 'https://www.wikidata.org/wiki/Q4723980', 'display_name': 'Algebra representation', 'level': 3, 'score': 0.3294857}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.070259154}, {'id': 'https://openalex.org/C99392333', 'wikidata': 'https://www.wikidata.org/wiki/Q5450385', 'display_name': 'Finite-rank operator', 'level': 3, 'score': 0.056156427}, {'id': 'https://openalex.org/C18903297', 'wikidata': 'https://www.wikidata.org/wiki/Q7150', 'display_name': 'Ecology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C41895202', 'wikidata': 'https://www.wikidata.org/wiki/Q8162', 'display_name': 'Linguistics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C138885662', 'wikidata': 'https://www.wikidata.org/wiki/Q5891', 'display_name': 'Philosophy', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C8010536', 'wikidata': 'https://www.wikidata.org/wiki/Q160398', 'display_name': 'Crystallography', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C86803240', 'wikidata': 'https://www.wikidata.org/wiki/Q420', 'display_name': 'Biology', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C132954091', 'wikidata': 'https://www.wikidata.org/wiki/Q194397', 'display_name': 'Banach space', 'level': 2, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://arxiv.org/pdf/1307.4696', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_indexed_in_scopus': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 16, 'referenced_works': ['https://openalex.org/W1524878283', 'https://openalex.org/W1544022757', 'https://openalex.org/W2001746077', 'https://openalex.org/W2012395494', 'https://openalex.org/W2012943431', 'https://openalex.org/W2019635767', 'https://openalex.org/W2025057664', 'https://openalex.org/W2043805475', 'https://openalex.org/W2072221883', 'https://openalex.org/W2262727861', 'https://openalex.org/W2320266418', 'https://openalex.org/W2330408611', 'https://openalex.org/W2331578546', 'https://openalex.org/W2399785464', 'https://openalex.org/W3038830718', 'https://openalex.org/W634797762'], 'related_works': ['https://openalex.org/W944696874', 'https://openalex.org/W33303354', 'https://openalex.org/W3106108077', 'https://openalex.org/W3102346101', 'https://openalex.org/W3022933764', 'https://openalex.org/W2985042631', 'https://openalex.org/W2963555735', 'https://openalex.org/W2804983273', 'https://openalex.org/W2504996155', 'https://openalex.org/W2500010951', 'https://openalex.org/W2256309348', 'https://openalex.org/W2143993516', 'https://openalex.org/W2126038653', 'https://openalex.org/W2119933950', 'https://openalex.org/W2027305287', 'https://openalex.org/W2010248635', 'https://openalex.org/W1985193145', 'https://openalex.org/W1977051412', 'https://openalex.org/W1677591053', 'https://openalex.org/W1636496677'], 'abstract_inverted_index': {'It': [0, 36], 'is': [1, 37], 'shown': [2], 'that': [3, 40], 'the': [4], '*-algebra': [5], 'of': [6], 'all': [7], '(closed': [8], 'densely': [9], 'defined': [10], 'linear)': [11], 'operators': [12], 'affiliated': [13], 'with': [14], 'a': [15, 23, 33], 'finite': [16], 'type': [17], 'I': [18], 'von': [19, 44], 'Neumann': [20, 45], 'algebra': [21], 'admits': [22], 'unique': [24], 'center-valued': [25], 'trace,': [26], 'which': [27], 'turns': [28], 'out': [29], 'to': [30], 'be,': [31], 'in': [32], 'sense,': [34], 'normal.': [35], 'also': [38], 'demonstrated': [39], 'for': [41], 'no': [42], 'other': [43], 'algebras': [46], 'similar': [47], 'constructions': [48], 'can': [49], 'be': [50], 'performed.': [51]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1511064543', 'counts_by_year': [{'year': 2016, 'cited_by_count': 1}], 'updated_date': '2025-01-22T04:10:17.387930', 'created_date': '2016-06-24'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
