{"id":"https://openalex.org/W1488344036","doi":"https://doi.org/10.1002/malq.201200093","title":"Uniformly convex Banach spaces are reflexive\u2014constructively","display_name":"Uniformly convex Banach spaces are reflexive\u2014constructively","publication_year":2013,"publication_date":"2013-08-01","ids":{"openalex":"https://openalex.org/W1488344036","doi":"https://doi.org/10.1002/malq.201200093","mag":"1488344036"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201200093","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201200093","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"article","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/A5053039771","display_name":"Douglas Bridges","orcid":null},"institutions":[{"id":"https://openalex.org/I185492890","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39","country_code":"NZ","type":"education","lineage":["https://openalex.org/I185492890"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Douglas S. Bridges","raw_affiliation_strings":["Department of Mathematics and Statistics University of Canterbury  Private Bag 4800 Christchurch New Zealand","Department of Mathematics & Statistics , University of Canterbury , Private Bag 4800, Christchurch , New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics University of Canterbury  Private Bag 4800 Christchurch New Zealand","institution_ids":["https://openalex.org/I185492890"]},{"raw_affiliation_string":"Department of Mathematics & Statistics , University of Canterbury , Private Bag 4800, Christchurch , New Zealand","institution_ids":["https://openalex.org/I185492890"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016735166","display_name":"Hajime Ishihara","orcid":"https://orcid.org/0000-0001-6074-4579"},"institutions":[{"id":"https://openalex.org/I177738480","display_name":"Japan Advanced Institute of Science and Technology","ror":"https://ror.org/03frj4r98","country_code":"JP","type":"education","lineage":["https://openalex.org/I177738480"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hajime Ishihara","raw_affiliation_strings":["School of Information Science Japan Advanced Institute of Science and Technology  Nomi Ishikawa 923\u20101292 Japan","School of Information Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa 923-1292, JAPAN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science Japan Advanced Institute of Science and Technology  Nomi Ishikawa 923\u20101292 Japan","institution_ids":["https://openalex.org/I177738480"]},{"raw_affiliation_string":"School of Information Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa 923-1292, JAPAN","institution_ids":["https://openalex.org/I177738480"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063156268","display_name":"Maarten McKubre\u2010Jordens","orcid":null},"institutions":[{"id":"https://openalex.org/I185492890","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39","country_code":"NZ","type":"education","lineage":["https://openalex.org/I185492890"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Maarten McKubre\u2010Jordens","raw_affiliation_strings":["Department of Mathematics and Statistics University of Canterbury  Private Bag 4800 Christchurch New Zealand","Department of Mathematics & Statistics , University of Canterbury , Private Bag 4800, Christchurch , New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics University of Canterbury  Private Bag 4800 Christchurch New Zealand","institution_ids":["https://openalex.org/I185492890"]},{"raw_affiliation_string":"Department of Mathematics & Statistics , University of Canterbury , Private Bag 4800, Christchurch , New Zealand","institution_ids":["https://openalex.org/I185492890"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063156268"],"corresponding_institution_ids":["https://openalex.org/I185492890"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03147609,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"4-5","first_page":"352","last_page":"356"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.967199981212616,"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":0.967199981212616,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9329000115394592,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uniformly-convex-space","display_name":"Uniformly convex space","score":0.8295819759368896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8242205381393433},{"id":"https://openalex.org/keywords/reflexive-space","display_name":"Reflexive space","score":0.7598459720611572},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7289923429489136},{"id":"https://openalex.org/keywords/reflexivity","display_name":"Reflexivity","score":0.6786074042320251},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6771684288978577},{"id":"https://openalex.org/keywords/eberlein\u2013\u0161mulian-theorem","display_name":"Eberlein\u2013\u0160mulian theorem","score":0.655052661895752},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5762627720832825},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4881637692451477},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39681777358055115},{"id":"https://openalex.org/keywords/lp-space","display_name":"Lp space","score":0.3430476784706116},{"id":"https://openalex.org/keywords/interpolation-space","display_name":"Interpolation space","score":0.30427682399749756},{"id":"https://openalex.org/keywords/functional-analysis","display_name":"Functional analysis","score":0.12197655439376831},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12027755379676819},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.0717519223690033}],"concepts":[{"id":"https://openalex.org/C123413131","wikidata":"https://www.wikidata.org/wiki/Q847535","display_name":"Uniformly convex space","level":5,"score":0.8295819759368896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8242205381393433},{"id":"https://openalex.org/C33549677","wikidata":"https://www.wikidata.org/wiki/Q2032198","display_name":"Reflexive space","level":5,"score":0.7598459720611572},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7289923429489136},{"id":"https://openalex.org/C13200473","wikidata":"https://www.wikidata.org/wiki/Q2747831","display_name":"Reflexivity","level":2,"score":0.6786074042320251},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6771684288978577},{"id":"https://openalex.org/C184908153","wikidata":"https://www.wikidata.org/wiki/Q2226650","display_name":"Eberlein\u2013\u0160mulian theorem","level":4,"score":0.655052661895752},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5762627720832825},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4881637692451477},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39681777358055115},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.3430476784706116},{"id":"https://openalex.org/C6183050","wikidata":"https://www.wikidata.org/wiki/Q3058180","display_name":"Interpolation space","level":4,"score":0.30427682399749756},{"id":"https://openalex.org/C55112680","wikidata":"https://www.wikidata.org/wiki/Q190549","display_name":"Functional analysis","level":3,"score":0.12197655439376831},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12027755379676819},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0717519223690033},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/malq.201200093","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201200093","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:philarchive.org/rec/BRIUCB","is_oa":false,"landing_page_url":"https://philarchive.org/rec/BRIUCB","pdf_url":null,"source":{"id":"https://openalex.org/S4306402130","display_name":"PhilPapers (PhilPapers Foundation)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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"},{"id":"pmh:oai:philpapers.org/rec/BRIUCB","is_oa":false,"landing_page_url":"https://philpapers.org/rec/BRIUCB","pdf_url":null,"source":{"id":"https://openalex.org/S4306402130","display_name":"PhilPapers (PhilPapers Foundation)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310502","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W569543113","https://openalex.org/W1980401155","https://openalex.org/W2011273996","https://openalex.org/W2036780301","https://openalex.org/W2040035010","https://openalex.org/W2067914884","https://openalex.org/W2083701356","https://openalex.org/W2084115686","https://openalex.org/W4239316923","https://openalex.org/W4256582740"],"related_works":["https://openalex.org/W1488344036","https://openalex.org/W2369289344","https://openalex.org/W2597141606","https://openalex.org/W2198155642","https://openalex.org/W951606502","https://openalex.org/W1961950596","https://openalex.org/W233199001","https://openalex.org/W4233503667","https://openalex.org/W1839439916","https://openalex.org/W4235408545"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,10,14,23],"natural":[3],"definition":[4],"of":[5,26],"what":[6],"it":[7],"means":[8],"in":[9],"constructive":[11,24],"context":[12],"for":[13],"Banach":[15,33],"space":[16],"to":[17],"be":[18],"reflexive,":[19],"and":[20],"then":[21],"prove":[22],"counterpart":[25],"the":[27],"Milman\u2010Pettis":[28],"theorem":[29],"that":[30],"uniformly":[31],"convex":[32],"spaces":[34],"are":[35],"reflexive.":[36]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
