{"id":"https://openalex.org/W1975135110","doi":"https://doi.org/10.1215/00294527-1715689","title":"Definable Operators on Hilbert Spaces","display_name":"Definable Operators on Hilbert Spaces","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1975135110","doi":"https://doi.org/10.1215/00294527-1715689","mag":"1975135110"},"language":"fr","primary_location":{"id":"doi:10.1215/00294527-1715689","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1715689","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-2/Definable-Operators-on-Hilbert-Spaces/10.1215/00294527-1715689.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-2/Definable-Operators-on-Hilbert-Spaces/10.1215/00294527-1715689.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064180225","display_name":"Isaac Goldbring","orcid":"https://orcid.org/0000-0003-0341-0251"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Isaac Goldbring","raw_affiliation_strings":["Department of Mathematics University of California, Los Angeles 520 Portola Plaza Box 951555 Los Angeles CA 90095-1555 USA","Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago 322 Science and Engineering Offices (M/C 249) 851 S. Morgan Street Chicago IL 60607-7045 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of California, Los Angeles 520 Portola Plaza Box 951555 Los Angeles CA 90095-1555 USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago 322 Science and Engineering Offices (M/C 249) 851 S. Morgan Street Chicago IL 60607-7045 USA","institution_ids":["https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064180225"],"corresponding_institution_ids":["https://openalex.org/I161318765","https://openalex.org/I39422238"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04500731,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"53","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9977999925613403,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9975000023841858,"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/linear-operators","display_name":"Linear operators","score":0.735813319683075},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.7322673797607422},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6739568114280701},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.6305183172225952},{"id":"https://openalex.org/keywords/compact-operator-on-hilbert-space","display_name":"Compact operator on Hilbert space","score":0.6125109195709229},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5737084746360779},{"id":"https://openalex.org/keywords/nuclear-operator","display_name":"Nuclear operator","score":0.5367817282676697},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5138207077980042},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.4884871244430542},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.41659241914749146},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3327534794807434},{"id":"https://openalex.org/keywords/compact-operator","display_name":"Compact operator","score":0.21702250838279724},{"id":"https://openalex.org/keywords/approximation-property","display_name":"Approximation property","score":0.2065226435661316},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14772272109985352},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.11141443252563477},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.06999757885932922},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.058059513568878174}],"concepts":[{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.735813319683075},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7322673797607422},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6739568114280701},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.6305183172225952},{"id":"https://openalex.org/C174058634","wikidata":"https://www.wikidata.org/wiki/Q5155314","display_name":"Compact operator on Hilbert space","level":4,"score":0.6125109195709229},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5737084746360779},{"id":"https://openalex.org/C22649536","wikidata":"https://www.wikidata.org/wiki/Q96396744","display_name":"Nuclear operator","level":4,"score":0.5367817282676697},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5138207077980042},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.4884871244430542},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.41659241914749146},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3327534794807434},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.21702250838279724},{"id":"https://openalex.org/C152306953","wikidata":"https://www.wikidata.org/wiki/Q621744","display_name":"Approximation property","level":3,"score":0.2065226435661316},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14772272109985352},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.11141443252563477},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.06999757885932922},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.058059513568878174},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1215/00294527-1715689","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1715689","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-2/Definable-Operators-on-Hilbert-Spaces/10.1215/00294527-1715689.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1010.2243","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1010.2243","pdf_url":"https://arxiv.org/pdf/1010.2243","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:1975135110","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1010.2243.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1336588250","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1336588250","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.751.5128","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.751.5128","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1010.2243.pdf","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/10771883","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Definable_Operators_on_Hilbert_Spaces/10771883","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"doi:10.48550/arxiv.1010.2243","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1010.2243","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":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":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1215/00294527-1715689","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1715689","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-2/Definable-Operators-on-Hilbert-Spaces/10.1215/00294527-1715689.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1975135110.pdf","grobid_xml":"https://content.openalex.org/works/W1975135110.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1542113445","https://openalex.org/W1769208762"],"related_works":["https://openalex.org/W2338788112","https://openalex.org/W2075055016","https://openalex.org/W2049285415","https://openalex.org/W2328704061","https://openalex.org/W2054155743","https://openalex.org/W2072543200","https://openalex.org/W231232394","https://openalex.org/W2081363185","https://openalex.org/W1595480090","https://openalex.org/W2079406128","https://openalex.org/W1993327392","https://openalex.org/W1964027864","https://openalex.org/W2167598465","https://openalex.org/W768618557","https://openalex.org/W2072599641","https://openalex.org/W2613011654","https://openalex.org/W2737784180","https://openalex.org/W2801100508","https://openalex.org/W2092327469","https://openalex.org/W2074129441"],"abstract_inverted_index":{"Let":[0],"H":[1,26],"be":[2],"an":[3],"infinite-dimensional":[4],"(real":[5],"or":[6],"complex)":[7],"Hilbert":[8],"space,":[9],"viewed":[10],"as":[11,27],"a":[12],"metric":[13],"structure":[14],"in":[15],"its":[16],"natural":[17],"signature.":[18],"We":[19],"characterize":[20],"the":[21,29],"definable":[22],"linear":[23],"operators":[24],"on":[25],"exactly":[28],"\"scalar":[30],"plus":[31],"compact\"":[32],"operators.":[33]},"counts_by_year":[],"updated_date":"2026-02-12T00:53:03.260389","created_date":"2025-10-10T00:00:00"}
