{"id":"https://openalex.org/W7213273699","doi":"https://doi.org/10.48550/arxiv.2609.14641","title":"Sphere version of Banach--Kadec--Paley theorem","display_name":"Sphere version of Banach--Kadec--Paley theorem","publication_year":2026,"publication_date":"2026-09-13","ids":{"openalex":"https://openalex.org/W7213273699","doi":"https://doi.org/10.48550/arxiv.2609.14641"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.14641","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14641","pdf_url":"https://arxiv.org/pdf/2609.14641","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.14641","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063236639","display_name":"Qingjin Cheng","orcid":"https://orcid.org/0000-0001-8015-877X","observed_orcids":["https://orcid.org/0000-0001-8015-877X"]},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cheng, Qingjin","raw_affiliation_strings":["School of Mathematical Sciences , Xiamen University , Xiamen 361005 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Xiamen University , Xiamen 361005 , China","institution_ids":["https://openalex.org/I191208505"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102218726","display_name":"Wuyi He","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"He, Wuyi","raw_affiliation_strings":["School of Mathematics and Statistics , Chongqing University of Posts and Telecommunications , Chongqing 400065 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Chongqing University of Posts and Telecommunications , Chongqing 400065 , China","institution_ids":["https://openalex.org/I10535382"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102867392","display_name":"Bo Xiang","orcid":"https://orcid.org/0000-0001-6649-8823","observed_orcids":["https://orcid.org/0000-0001-6649-8823"]},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiang, Bo","raw_affiliation_strings":["School of Mathematical Sciences , Xiamen University , Xiamen 361005 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Xiamen University , Xiamen 361005 , China","institution_ids":["https://openalex.org/I191208505"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":false,"primary_topic":{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9961000084877014,"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":0.9961000084877014,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.002400000113993883,"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"}},{"id":"https://openalex.org/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":9.999999747378752e-05,"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/unit-sphere","display_name":"unit sphere","score":0.800000011920929},{"id":"https://openalex.org/keywords/lp-spaces","display_name":"Lp spaces","score":0.7590000033378601},{"id":"https://openalex.org/keywords/modulus-of-continuity","display_name":"modulus of continuity","score":0.7839999794960022},{"id":"https://openalex.org/keywords/concentration-inequalities","display_name":"concentration inequalities","score":0.9279999732971191}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8191999793052673},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8052999973297119},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7009999752044678},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.6992999911308289},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5922999978065491},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5059999823570251},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.49720001220703125},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44339999556541443},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.414000004529953},{"id":"https://openalex.org/C145084290","wikidata":"https://www.wikidata.org/wiki/Q2713824","display_name":"Metric map","level":4,"score":0.40059998631477356},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.3878999948501587},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.38420000672340393},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3287000060081482},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C41261874","wikidata":"https://www.wikidata.org/wiki/Q3855712","display_name":"Intrinsic metric","level":4,"score":0.27070000767707825}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.14641","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14641","pdf_url":"https://arxiv.org/pdf/2609.14641","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"},{"id":"doi:10.48550/arxiv.2609.14641","doi":"https://doi.org/10.48550/arxiv.2609.14641","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.14641","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.14641","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14641","pdf_url":"https://arxiv.org/pdf/2609.14641","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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213273699.pdf","grobid_xml":"https://content.openalex.org/works/W7213273699.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7098420602","https://openalex.org/W7099322569","https://openalex.org/W1965963638","https://openalex.org/W1615887844","https://openalex.org/W1498360899","https://openalex.org/W2964154786","https://openalex.org/W2068137519","https://openalex.org/W1982130705","https://openalex.org/W1996432338","https://openalex.org/W1119891199"],"abstract_inverted_index":{"We":[0],"study":[1],"almost":[2,36,54],"Lipschitz":[3,37,55],"embeddings":[4],"in":[5],"the":[6,23,30,53,61,105],"quantitative":[7,71],"geometry":[8,56,107],"of":[9,12,22,57,65,75,77,108],"unit":[10,31],"spheres":[11],"classical":[13,24],"\\(L_p\\)-spaces.":[14,66],"Our":[15],"main":[16],"result":[17],"is":[18],"a":[19,47],"sphere":[20,32,78],"version":[21],"Banach--Kadec--Paley":[25],"theorem:":[26],"for":[27,73],"\\(1\\le":[28],"p,q<\\infty\\),":[29],"\\(S_{L_q}\\)":[33],"admits":[34,46],"an":[35],"embedding":[38,49],"into":[39,50],"\\(L_p\\)":[40],"if":[41,44],"and":[42,92],"only":[43],"\\(L_q\\)":[45],"linear":[48,63],"\\(L_p\\).":[51],"Consequently,":[52],"\\(L_p\\)-spheres":[58],"completely":[59],"determines":[60],"underlying":[62],"structure":[64],"The":[67],"proof":[68],"relies":[69],"on":[70,104],"estimates":[72,81],"moduli":[74],"continuity":[76],"mappings.":[79],"These":[80],"are":[82],"derived":[83],"from":[84],"Kalton--Randrianarivony's":[85],"concentration":[86],"inequalities,":[87],"Mendel--Naor's":[88],"metric":[89,95],"cotype":[90],"inequality,":[91],"Naor's":[93],"sharp":[94,102],"\\(X_p\\)":[96],"inequality.":[97],"They":[98],"also":[99],"yield":[100],"several":[101],"results":[103],"H\u00f6lder":[106],"\\(L_p\\)-spheres.":[109]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-16T00:00:00"}