{"id":"https://openalex.org/W7078600239","doi":null,"title":"Tensor products of measurable Banach bundles","display_name":"Tensor products of measurable Banach bundles","publication_year":2025,"publication_date":"2025-08-27","ids":{"openalex":"https://openalex.org/W7078600239"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2508.19635","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2508.19635","pdf_url":"https://arxiv.org/pdf/2508.19635","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2508.19635","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5145617815","display_name":"Milica Cakovi\u0107","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cakovi\u0107, Milica","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075447744","display_name":"Danka Lu\u010di\u0107","orcid":"https://orcid.org/0000-0003-0634-8318","observed_orcids":["https://orcid.org/0000-0003-0634-8318"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lu\u010di\u0107, Danka","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5009413352","display_name":"Enrico Pasqualetto","orcid":"https://orcid.org/0000-0002-7532-5577","observed_orcids":["https://orcid.org/0000-0002-7532-5577"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pasqualetto, Enrico","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9502000212669373,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9502000212669373,"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":0.04820000007748604,"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":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/injective-tensor-product","display_name":"injective tensor product","score":0.9110000133514404},{"id":"https://openalex.org/keywords/projective-tensor-product","display_name":"projective tensor product","score":1.0},{"id":"https://openalex.org/keywords/countably-generated-modules","display_name":"countably generated modules","score":0.6010000109672546},{"id":"https://openalex.org/keywords/probability-spaces","display_name":"probability spaces","score":0.5009999871253967}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7736999988555908},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.7605999708175659},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.6380000114440918},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6226000189781189},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6140999794006348},{"id":"https://openalex.org/C93776189","wikidata":"https://www.wikidata.org/wiki/Q1404488","display_name":"Tensor product of Hilbert spaces","level":4,"score":0.5748000144958496},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5113000273704529},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5038999915122986},{"id":"https://openalex.org/C101783463","wikidata":"https://www.wikidata.org/wiki/Q3406761","display_name":"Tensor product of modules","level":5,"score":0.4016999900341034},{"id":"https://openalex.org/C165593952","wikidata":"https://www.wikidata.org/wiki/Q3554819","display_name":"Banach manifold","level":4,"score":0.392300009727478},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.35839998722076416},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.31310001015663147},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C80739010","wikidata":"https://www.wikidata.org/wiki/Q6029720","display_name":"Infinite-dimensional vector function","level":5,"score":0.3052999973297119},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29490000009536743},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.29420000314712524},{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C41678559","wikidata":"https://www.wikidata.org/wiki/Q7700713","display_name":"Tensor product of algebras","level":5,"score":0.2865000069141388},{"id":"https://openalex.org/C178099376","wikidata":"https://www.wikidata.org/wiki/Q7825044","display_name":"Topological tensor product","level":4,"score":0.2854999899864197},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2728999853134155},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.26460000872612},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2578999996185303}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:arXiv.org:2508.19635","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2508.19635","pdf_url":"https://arxiv.org/pdf/2508.19635","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2508.19635","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2508.19635","pdf_url":"https://arxiv.org/pdf/2508.19635","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1],"injective":[2,91,123],"and":[3,40,55,85,92,100,129],"projective":[4,93,131],"tensor":[5,94,124,132],"products":[6],"of":[7,78,97,106,121,137],"measurable":[8,16,34,71],"Banach":[9,17,35,72],"bundles.":[10],"More":[11],"precisely,":[12],"given":[13],"two":[14,33,138],"separable":[15],"bundles":[18,36],"${\\bf":[19,21,37,41,62,74],"E}$,":[20],"F}$":[22,39,43],"defined":[23],"over":[24,44],"a":[25,70,118],"probability":[26],"space":[27,77],"$({\\rm":[28,45],"X},\u03a3,\\mathfrak":[29,46],"m)$,":[30],"we":[31],"construct":[32],"E}\\hat\\otimes_\\varepsilon{\\bf":[38,51],"E}\\hat\\otimes_\u03c0{\\bf":[42,57],"m)$":[47],"such":[48],"that":[49],"$\u0393({\\bf":[50,56,82,86,98,101],"F})\\cong\u0393({\\bf":[52,58],"E})\\hat\\otimes_\\varepsilon\u0393({\\bf":[53,83],"F})$":[54,84,88,102],"E})\\hat\\otimes_\u03c0\u0393({\\bf":[59,87],"F})$,":[60],"where":[61],"G}\\mapsto\u0393({\\bf":[63],"G})$":[64],"is":[65],"the":[66,90,104,122,130],"map":[67],"assigning":[68],"to":[69],"bundle":[73],"G}$":[75],"its":[76],"$L^\\infty(\\mathfrak":[79,107,109,140,142],"m)$-sections,":[80],"while":[81],"denote":[89],"products,":[95],"respectively,":[96],"E})$":[99],"in":[103],"sense":[105],"m)$-Banach":[108,141],"m)$-modules.":[110],"In":[111],"combination":[112],"with":[113],"previous":[114],"results,":[115],"this":[116],"provides":[117],"fiberwise":[119],"representation":[120],"product":[125,133],"$\\mathscr":[126,134,144,146],"M\\hat\\otimes_\\varepsilon\\mathscr":[127],"N$":[128,136],"M\\hat\\otimes_\u03c0\\mathscr":[135],"countably-generated":[139],"m)$-modules":[143],"M$,":[145],"N$.":[147]},"counts_by_year":[],"updated_date":"2026-10-13T10:08:12.033832","created_date":"2025-10-10T00:00:00"}