{"id":"https://openalex.org/W2894099630","doi":"https://doi.org/10.1080/00029890.2018.1496762","title":"Simple Proofs of the Uniform Convexity of<i>L<sup>p</sup></i>and the Riesz Representation Theorem for<i>L<sup>p</sup></i>","display_name":"Simple Proofs of the Uniform Convexity of<i>L<sup>p</sup></i>and the Riesz Representation Theorem for<i>L<sup>p</sup></i>","publication_year":2018,"publication_date":"2018-09-14","ids":{"openalex":"https://openalex.org/W2894099630","doi":"https://doi.org/10.1080/00029890.2018.1496762","mag":"2894099630"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2018.1496762","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1496762","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","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/A5010267090","display_name":"Naoki Shioji","orcid":"https://orcid.org/0000-0003-3392-7577"},"institutions":[{"id":"https://openalex.org/I180203408","display_name":"Yokohama National University","ror":"https://ror.org/03zyp6p76","country_code":"JP","type":"education","lineage":["https://openalex.org/I180203408"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Naoki Shioji","raw_affiliation_strings":["Department of Mathematics, Faculty of Engineering, Yokohama National University, Tokiwadai, Hodogaya, Yokohama 240-8501, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Engineering, Yokohama National University, Tokiwadai, Hodogaya, Yokohama 240-8501, Japan","institution_ids":["https://openalex.org/I180203408"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010267090"],"corresponding_institution_ids":["https://openalex.org/I180203408"],"apc_list":null,"apc_paid":null,"fwci":0.4039,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64601735,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"125","issue":"8","first_page":"733","last_page":"738"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9947999715805054,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/convexity","display_name":"Convexity","score":0.8161461353302002},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7710272669792175},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.7560815215110779},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7009827494621277},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5907769203186035},{"id":"https://openalex.org/keywords/riesz-representation-theorem","display_name":"Riesz representation theorem","score":0.5330100655555725},{"id":"https://openalex.org/keywords/m.-riesz-extension-theorem","display_name":"M. Riesz extension theorem","score":0.4598868787288666},{"id":"https://openalex.org/keywords/representation-theorem","display_name":"Representation theorem","score":0.4476161599159241},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4289485514163971},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.37307673692703247},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06460696458816528},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.045030683279037476},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.04343467950820923}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8161461353302002},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7710272669792175},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7560815215110779},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7009827494621277},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5907769203186035},{"id":"https://openalex.org/C113675457","wikidata":"https://www.wikidata.org/wiki/Q1357684","display_name":"Riesz representation theorem","level":2,"score":0.5330100655555725},{"id":"https://openalex.org/C56969512","wikidata":"https://www.wikidata.org/wiki/Q3527217","display_name":"M. Riesz extension theorem","level":2,"score":0.4598868787288666},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.4476161599159241},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4289485514163971},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.37307673692703247},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06460696458816528},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.045030683279037476},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.04343467950820923},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2018.1496762","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1496762","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W39337161","https://openalex.org/W1543889132","https://openalex.org/W1569319789","https://openalex.org/W1582706191","https://openalex.org/W1594563152","https://openalex.org/W1604410016","https://openalex.org/W1654572409","https://openalex.org/W1679714949","https://openalex.org/W1966675143","https://openalex.org/W2002713832","https://openalex.org/W2005848700","https://openalex.org/W2011273996","https://openalex.org/W2014332282","https://openalex.org/W2107106142","https://openalex.org/W2121292395","https://openalex.org/W2129195101","https://openalex.org/W2465542672","https://openalex.org/W3106121889","https://openalex.org/W4243856850"],"related_works":["https://openalex.org/W2015288988","https://openalex.org/W2084899942","https://openalex.org/W2155782347","https://openalex.org/W2134382530","https://openalex.org/W3023681660","https://openalex.org/W4294226274","https://openalex.org/W2039801349","https://openalex.org/W4206393249","https://openalex.org/W4243698900","https://openalex.org/W2076579365"],"abstract_inverted_index":{"We":[0],"give":[1],"elementary":[2],"and":[3,17],"self-contained":[4],"proofs":[5],"of":[6],"the":[7,10],"facts":[8],"that":[9],"Lp":[11],"space":[12,20],"with":[13],"is":[14,21],"uniformly":[15],"convex":[16],"its":[18],"dual":[19],"isometrically":[22],"isomorphic":[23],"to":[24],".":[25]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
