{"id":"https://openalex.org/W7223067973","doi":"https://doi.org/10.48550/arxiv.2610.26738","title":"A two-dimensional subspace of $\\ell_\\infty^3$ has a unique operator space structure if and only if it is isometric to $\\ell_\\infty^2$","display_name":"A two-dimensional subspace of $\\ell_\\infty^3$ has a unique operator space structure if and only if it is isometric to $\\ell_\\infty^2$","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7223067973","doi":"https://doi.org/10.48550/arxiv.2610.26738"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.26738","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26738","pdf_url":"https://arxiv.org/pdf/2610.26738","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/2610.26738","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159110134","display_name":"Rajeev Gupta","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gupta, Rajeev","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079341017","display_name":"\u200eArpita Mal","orcid":"https://orcid.org/0000-0002-3861-7140","observed_orcids":["https://orcid.org/0000-0002-3861-7140"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mal, Arpita","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087028802","display_name":"Gadadhar Misra","orcid":"https://orcid.org/0000-0001-8096-2039","observed_orcids":["https://orcid.org/0000-0001-8096-2039"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Misra, Gadadhar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004889029","display_name":"S. Ray","orcid":"https://orcid.org/0000-0003-0536-9491","observed_orcids":["https://orcid.org/0000-0003-0536-9491"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ray, Samya Kumar","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":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":0.6820999979972839,"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":0.6820999979972839,"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":0.29789999127388,"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":0.010999999940395355,"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/l-infinity-spaces","display_name":"L-infinity spaces","score":0.703000009059906},{"id":"https://openalex.org/keywords/extreme-points","display_name":"extreme points","score":0.7609999775886536},{"id":"https://openalex.org/keywords/non-normal-matrices","display_name":"non-normal matrices","score":0.6470000147819519}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.771399974822998},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7296000123023987},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5971999764442444},{"id":"https://openalex.org/C176691602","wikidata":"https://www.wikidata.org/wiki/Q7097841","display_name":"Operator space","level":4,"score":0.5514000058174133},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5228999853134155},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.49619999527931213},{"id":"https://openalex.org/C2992500303","wikidata":"https://www.wikidata.org/wiki/Q5680845","display_name":"Operator matrix","level":2,"score":0.4855000078678131},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4715000092983246},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4616999924182892},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.45669999718666077},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4268999993801117},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.41999998688697815},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41269999742507935},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.4088999927043915},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.3885999917984009},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3797000050544739},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.37400001287460327},{"id":"https://openalex.org/C103486182","wikidata":"https://www.wikidata.org/wiki/Q1216236","display_name":"Isometric exercise","level":2,"score":0.367000013589859},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.352400004863739},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.351500004529953},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.350600004196167},{"id":"https://openalex.org/C152306953","wikidata":"https://www.wikidata.org/wiki/Q621744","display_name":"Approximation property","level":3,"score":0.3416000008583069},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.3407000005245209},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30399999022483826},{"id":"https://openalex.org/C82916341","wikidata":"https://www.wikidata.org/wiki/Q6934990","display_name":"Multiplication operator","level":3,"score":0.29109999537467957},{"id":"https://openalex.org/C65630602","wikidata":"https://www.wikidata.org/wiki/Q2278680","display_name":"Shift operator","level":4,"score":0.28630000352859497},{"id":"https://openalex.org/C2776551381","wikidata":"https://www.wikidata.org/wiki/Q6680542","display_name":"Lorentz space","level":3,"score":0.2768999934196472}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.26738","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26738","pdf_url":"https://arxiv.org/pdf/2610.26738","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.2610.26738","doi":"https://doi.org/10.48550/arxiv.2610.26738","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.26738","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:2610.26738","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26738","pdf_url":"https://arxiv.org/pdf/2610.26738","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":[{"id":"https://openalex.org/G8749306478","display_name":null,"funder_award_id":"DST/INSPIRE/04/2022/001207","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"}],"funders":[{"id":"https://openalex.org/F4320306227","display_name":"Arthritis National Research Foundation","ror":"https://ror.org/03abbex33"},{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223067973.pdf","grobid_xml":"https://content.openalex.org/works/W7223067973.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7167965371","https://openalex.org/W7220650000"],"related_works":["https://openalex.org/W7220650000","https://openalex.org/W3016918825","https://openalex.org/W4394666857","https://openalex.org/W2360955154","https://openalex.org/W7093592300","https://openalex.org/W2983384381","https://openalex.org/W1996341629","https://openalex.org/W2089217554","https://openalex.org/W1637852107","https://openalex.org/W2084110841"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"a":[3,10],"two-dimensional":[4,69],"complex":[5,92],"subspace":[6,70],"of":[7,33,50,71,84],"$\\ell_\\infty^3$":[8,72],"carries":[9],"unique":[11],"operator":[12,86],"space":[13,87],"structure":[14,88],"if":[15,18],"and":[16],"only":[17],"it":[19],"is":[20,27,61],"isometric":[21],"to":[22],"$\\ell_\\infty^2$;":[23],"the":[24,28,34,51,57,74,77,85],"``if''":[25],"half":[26],"And\u00f4's":[29],"theorem.":[30],"For":[31],"each":[32],"remaining":[35],"spaces":[36],"we":[37],"exhibit":[38],"an":[39,47],"explicit":[40],"non-normal":[41],"$Y":[42],"\\in":[43],"\\mathcal{M}_2$,":[44],"with":[45],"$(I,Y)$":[46],"extreme":[48],"point":[49],"associated":[52],"matrix":[53],"ball,":[54],"for":[55,89],"which":[56],"induced":[58],"linear":[59],"map":[60],"contractive":[62],"but":[63],"not":[64,81],"completely":[65],"contractive.":[66],"Since":[67],"every":[68],"has":[73],"$2$-summing":[75,78],"property,":[76],"property":[79],"does":[80],"imply":[82],"uniqueness":[83],"two":[90],"dimensional":[91],"Banach":[93],"spaces.":[94]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}
