{"id":"https://openalex.org/W7203871769","doi":"https://doi.org/10.48550/arxiv.2608.19286","title":"Minimum attaining operators on reducing subspaces: Spectral structure and density","display_name":"Minimum attaining operators on reducing subspaces: Spectral structure and density","publication_year":2026,"publication_date":"2026-08-19","ids":{"openalex":"https://openalex.org/W7203871769","doi":"https://doi.org/10.48550/arxiv.2608.19286"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.19286","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.19286","pdf_url":"https://arxiv.org/pdf/2608.19286","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/2608.19286","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123155694","display_name":"Puspendu Nag","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Puspendu, Nag","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5124706198","display_name":"Ramesh Golla","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ramesh, Golla","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":2,"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":0.5619999766349792,"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":0.5619999766349792,"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":0.38260000944137573,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.04639999940991402,"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/reducing-subspaces","display_name":"reducing subspaces","score":0.949999988079071},{"id":"https://openalex.org/keywords/spectroscopic-characterization","display_name":"spectroscopic characterization","score":0.6909999847412109},{"id":"https://openalex.org/keywords/positive-operators","display_name":"positive operators","score":0.9599999785423279},{"id":"https://openalex.org/keywords/norm-attainment","display_name":"norm attainment","score":0.421999990940094},{"id":"https://openalex.org/keywords/finite-rank-perturbations","display_name":"finite rank perturbations","score":0.8240000009536743},{"id":"https://openalex.org/keywords/compact-perturbations","display_name":"compact perturbations","score":0.9980000257492065},{"id":"https://openalex.org/keywords/normal-operators","display_name":"normal operators","score":0.9509999752044678},{"id":"https://openalex.org/keywords/von-neumann-algebras","display_name":"von Neumann algebras","score":0.7839999794960022}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8058000206947327},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.7096999883651733},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6521999835968018},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.5720000267028809},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5393000245094299},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.5357999801635742},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4767000079154968},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.46309998631477356},{"id":"https://openalex.org/C22649536","wikidata":"https://www.wikidata.org/wiki/Q96396744","display_name":"Nuclear operator","level":4,"score":0.4569000005722046},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.45089998841285706},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4212999939918518},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.42089998722076416},{"id":"https://openalex.org/C174058634","wikidata":"https://www.wikidata.org/wiki/Q5155314","display_name":"Compact operator on Hilbert space","level":4,"score":0.4174000024795532},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39890000224113464},{"id":"https://openalex.org/C24250787","wikidata":"https://www.wikidata.org/wiki/Q7269510","display_name":"Quasinormal operator","level":4,"score":0.39739999175071716},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3840999901294708},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.37929999828338623},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3393000066280365},{"id":"https://openalex.org/C2992500303","wikidata":"https://www.wikidata.org/wiki/Q5680845","display_name":"Operator matrix","level":2,"score":0.32249999046325684},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2754000127315521},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.27309998869895935},{"id":"https://openalex.org/C180375552","wikidata":"https://www.wikidata.org/wiki/Q2635326","display_name":"Structured program theorem","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.2581000030040741},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C60064506","wikidata":"https://www.wikidata.org/wiki/Q1262627","display_name":"Rigged Hilbert space","level":4,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.19286","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.19286","pdf_url":"https://arxiv.org/pdf/2608.19286","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.2608.19286","doi":"https://doi.org/10.48550/arxiv.2608.19286","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.19286","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:2608.19286","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.19286","pdf_url":"https://arxiv.org/pdf/2608.19286","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/W7203871769.pdf","grobid_xml":"https://content.openalex.org/works/W7203871769.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4387716591","https://openalex.org/W2797922648","https://openalex.org/W7006119518","https://openalex.org/W2030215819","https://openalex.org/W2470304933","https://openalex.org/W7214912302","https://openalex.org/W3001177898","https://openalex.org/W4416076443","https://openalex.org/W4415903863","https://openalex.org/W3006720145"],"abstract_inverted_index":{"In":[0],"this":[1,139,179],"article,":[2],"we":[3,111,147],"introduce":[4],"and":[5,41,63,83,97,118,121,162],"study":[6],"the":[7,34,86,98,133,164,170],"class":[8,31,99,140],"$\\mathcal{M}_r(H)$":[9,61,96,124],"of":[10,36,50,78,100,136,169],"minimum":[11,28,38,42],"attaining":[12,39,43,102],"operators":[13,40,52,101,137,150,159],"on":[14,105,160],"a":[15,47,55,70,76,93,142,154],"separable":[16],"Hilbert":[17],"space":[18],"$H$":[19],"whose":[20],"restrictions":[21],"to":[22,60,183],"every":[23,106],"nonzero":[24,81,107],"reducing":[25,108],"subspace":[26],"are":[27],"attaining.":[29],"This":[30],"lies":[32],"between":[33,95],"classes":[35],"absolutely":[37],"operators.":[44],"We":[45,90,130],"establish":[46,92,132],"spectral":[48],"characterization":[49,156],"positive":[51,56],"in":[53,85,128,138,151,167],"$\\mathcal{M}_r(H)$:":[54],"operator":[57,88],"$T$":[58,182],"belongs":[59],"if":[62,65],"only":[64],"$T=\\sum_{\u03bb\\in\u039b}\u03bbP_\u03bb$,":[66],"where":[67],"$\u039b\\subseteq[0,\\|T\\|]$":[68],"is":[69,75,125],"countable":[71],"well-ordered":[72],"set,":[73],"$(P_\u03bb)_{\u03bb\\in\u039b}$":[74],"family":[77],"mutually":[79],"orthogonal":[80],"projections,":[82],"$\\sum_{\u03bb\\in\u039b}P_\u03bb=I$":[84],"strong":[87],"topology.":[89],"also":[91,131],"connection":[94],"their":[103],"norm":[104,126,134],"subspace.":[109],"Further,":[110],"obtain":[112,153],"stability":[113],"results":[114],"under":[115],"suitable":[116],"finite-rank":[117],"compact":[119],"perturbations,":[120],"prove":[122],"that":[123,178],"dense":[127],"$\\mathcal{B}(H)$.":[129],"density":[135],"having":[141],"nontrivial":[143],"invariant":[144],"half-space.":[145],"Finally,":[146],"characterize":[148,163],"normal":[149],"$\\mathcal{M}_r(H)$,":[152],"corresponding":[155],"for":[157],"multiplication":[158],"$L^2(\\mathbb{T})$,":[161],"condition":[165,180],"$\\mathcal{R}_T=\\mathcal{R}_{|T|}$":[166],"terms":[168],"von":[171],"Neumann":[172],"algebra":[173],"generated":[174],"by":[175],"$|T|$,":[176],"showing":[177],"forces":[181],"be":[184],"normal.":[185]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-22T00:00:00"}