{"id":"https://openalex.org/W7223914951","doi":"https://doi.org/10.48550/arxiv.2610.34152","title":"Well located Banach spaces - A combined approach to L_1- preduals and Hilbert space","display_name":"Well located Banach spaces - A combined approach to L_1- preduals and Hilbert space","publication_year":2026,"publication_date":"2026-10-25","ids":{"openalex":"https://openalex.org/W7223914951","doi":"https://doi.org/10.48550/arxiv.2610.34152"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.34152","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34152","pdf_url":"https://arxiv.org/pdf/2610.34152","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.34152","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159758562","display_name":"M A Sofi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I135388327","display_name":"University of Kashmir","ror":"https://ror.org/032xfst36","country_code":"IN","type":"education","lineage":["https://openalex.org/I135388327"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Sofi, M A","raw_affiliation_strings":["Department of Mathematics University of Kashmir , Srinagar"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Kashmir , Srinagar","institution_ids":["https://openalex.org/I135388327"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5159758562"],"corresponding_institution_ids":["https://openalex.org/I135388327"],"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":1.0,"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":1.0,"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":0.0,"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":0.0,"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/hilbert-spaces","display_name":"Hilbert spaces","score":0.9309999942779541},{"id":"https://openalex.org/keywords/complemented-subspaces","display_name":"complemented subspaces","score":0.7720000147819519},{"id":"https://openalex.org/keywords/operator-ideals","display_name":"operator ideals","score":0.8769999742507935}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7662000060081482},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6819999814033508},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.6552000045776367},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6474000215530396},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6456999778747559},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6416000127792358},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5231000185012817},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.46959999203681946},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4648999869823456},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.4115000069141388},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3977000117301941},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3962000012397766},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.3961000144481659},{"id":"https://openalex.org/C147493315","wikidata":"https://www.wikidata.org/wiki/Q3554824","display_name":"Hilbert manifold","level":3,"score":0.39489999413490295},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.391400009393692},{"id":"https://openalex.org/C176691602","wikidata":"https://www.wikidata.org/wiki/Q7097841","display_name":"Operator space","level":4,"score":0.3619000017642975},{"id":"https://openalex.org/C165593952","wikidata":"https://www.wikidata.org/wiki/Q3554819","display_name":"Banach manifold","level":4,"score":0.3400000035762787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32440000772476196},{"id":"https://openalex.org/C80739010","wikidata":"https://www.wikidata.org/wiki/Q6029720","display_name":"Infinite-dimensional vector function","level":5,"score":0.3109000027179718},{"id":"https://openalex.org/C6183050","wikidata":"https://www.wikidata.org/wiki/Q3058180","display_name":"Interpolation space","level":4,"score":0.29910001158714294},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26330000162124634},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.25360000133514404},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.34152","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34152","pdf_url":"https://arxiv.org/pdf/2610.34152","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.2610.34152","doi":"https://doi.org/10.48550/arxiv.2610.34152","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.34152","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.34152","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34152","pdf_url":"https://arxiv.org/pdf/2610.34152","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/W7223914951.pdf","grobid_xml":"https://content.openalex.org/works/W7223914951.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3194680486","https://openalex.org/W2049815761","https://openalex.org/W7096552734","https://openalex.org/W2563935054","https://openalex.org/W1986585583","https://openalex.org/W6967044418","https://openalex.org/W3043123223","https://openalex.org/W4416434650","https://openalex.org/W1983898092","https://openalex.org/W3002318422"],"abstract_inverted_index":{"In":[0,122],"the":[1,7,15,19,34,47,55,63,72,98,139,157,165,170,176,184,206],"description":[2],"of":[3,11,22,25,29,36,40,58,74,100,159,172,180,190,200,205,208],"L_1-":[4,173],"preduals":[5,174],"on":[6,14],"one":[8,17],"hand":[9],"and":[10,179],"Hilbert":[12,94,181,201],"spaces,":[13,182],"other,":[16],"encounters":[18],"surprising":[20],"appearance":[21],"similar":[23],"classes":[24,39,57],"operators":[26],"in":[27,33,71,97,175,183,203],"terms":[28,204],"their":[30],"extendibility":[31,207],"properties":[32,49,132,167],"setting":[35],"these":[37],"two":[38,56],"spaces.":[41,65],"It":[42,66,153],"also":[43],"turns":[44,113,154],"out":[45,114,155],"that":[46,70,115,135,156],"extension":[48],"are":[50,60,168,194],"closely":[51],"tied":[52],"to":[53,89,196],"how":[54],"spaces":[59,161,202],"positioned":[61,78],"inside":[62,79,108,138],"ambient":[64,140],"is":[67,106,117],"well":[68],"known":[69],"case":[73,99,178],"all":[75,109],"subspaces":[76],"being":[77,91],"a":[80,85,93,101,143,150],"larger":[81],"space":[82,95,103,141],"Z":[83,90],"as":[84,133,142,149],"complemented":[86,107,145],"subspace":[87,146],"leads":[88],"(isomorphically)":[92],"whereas":[96],"Banach":[102,120,160],"X":[104,116,136,162],"which":[105],"its":[110],"superspaces,":[111],"it":[112],"an":[118,187],"injective":[119],"space.":[121],"this":[123,191],"paper,":[124],"we":[125,193],"shall":[126],"be":[127],"concerned":[128],"mostly":[129],"with":[130],"such":[131],"demanding":[134],"sit":[137],"locally":[144],"(and":[147],"sometimes":[148],"Lipchitz":[151],"retract).":[152],"class":[158,171],"determined":[163],"by":[164],"indicated":[166],"precisely":[169],"former":[177],"latter.":[185],"As":[186],"important":[188],"consequence":[189],"approach,":[192],"led":[195],"several":[197],"new":[198],"characterisations":[199],"bounded":[209],"linear":[210],"maps":[211],"coming":[212],"from":[213],"well-known":[214],"operator":[215],"(nonlinear":[216],"operator)":[217],"ideals.":[218]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2026-10-28T00:00:00"}
