{"id":"https://openalex.org/W7213332005","doi":"https://doi.org/10.48550/arxiv.2609.15057","title":"Applications of the Projection Characterization and Symmetry Bootstrap for Operators that are Nearby Commuting Operators","display_name":"Applications of the Projection Characterization and Symmetry Bootstrap for Operators that are Nearby Commuting Operators","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213332005","doi":"https://doi.org/10.48550/arxiv.2609.15057"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.15057","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15057","pdf_url":"https://arxiv.org/pdf/2609.15057","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/2609.15057","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151760535","display_name":"David Herrera","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Herrera, David","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5151760535"],"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.7440999746322632,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.7440999746322632,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.1281999945640564,"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":0.03660000115633011,"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/stability-theorems","display_name":"stability theorems","score":0.8970000147819519},{"id":"https://openalex.org/keywords/unitary-operators","display_name":"unitary operators","score":0.7110000252723694},{"id":"https://openalex.org/keywords/self-adjoint-operators","display_name":"self-adjoint operators","score":0.9850000143051147},{"id":"https://openalex.org/keywords/matrix-operators","display_name":"matrix operators","score":0.3269999921321869}],"concepts":[{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.8253999948501587},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6819000244140625},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6718999743461609},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.663100004196167},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.6402999758720398},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5424000024795532},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.525600016117096},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.5041999816894531},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4864000082015991},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43939998745918274},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.42739999294281006},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.40689998865127563},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34439998865127563},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.2888000011444092},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.2824999988079071}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.15057","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15057","pdf_url":"https://arxiv.org/pdf/2609.15057","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.2609.15057","doi":"https://doi.org/10.48550/arxiv.2609.15057","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.15057","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:2609.15057","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15057","pdf_url":"https://arxiv.org/pdf/2609.15057","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/G6446429780","display_name":"Variational Problems, Stability and Dynamics","funder_award_id":"1764254","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213332005.pdf","grobid_xml":"https://content.openalex.org/works/W7213332005.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W2129334098","https://openalex.org/W2922119167","https://openalex.org/W4281993361","https://openalex.org/W4311416215","https://openalex.org/W4311431729","https://openalex.org/W4390723191","https://openalex.org/W4399553853","https://openalex.org/W4416292099"],"related_works":["https://openalex.org/W4405957111","https://openalex.org/W2003900729","https://openalex.org/W2038195941","https://openalex.org/W2031194142","https://openalex.org/W4416292099","https://openalex.org/W1976745974","https://openalex.org/W2609071097","https://openalex.org/W1977597076","https://openalex.org/W4403551946","https://openalex.org/W2003995688"],"abstract_inverted_index":{"This":[0],"paper":[1],"applies":[2],"the":[3,7,75],"Projection":[4],"Characterization":[5],"and":[6,45],"Symmetry":[8],"Bootstrap":[9],"for":[10,61,66,72,79],"two":[11],"operators":[12,22,41,77],"$A,":[13],"B$":[14],"(with":[15,25],"$A$":[16],"unitary":[17,27],"or":[18,28],"self-adjoint)":[19,29],"nearby":[20],"commuting":[21,38],"$A',":[23],"B'$":[24],"$A'$":[26],"from":[30],"arXiv:2412.20795":[31],"to":[32,35,51],"problems":[33],"related":[34],"structured":[36],"almost":[37,43,48],"unitaries,":[39],"self-adjoint":[40],"that":[42,47,84],"anti-commute,":[44],"unitaries":[46],"commute":[49],"up":[50],"a":[52],"rational":[53],"phase.":[54],"We":[55,68],"prove":[56],"several":[57,80],"new":[58],"stability":[59,82],"theorems":[60,83],"these":[62],"types":[63],"of":[64],"relations":[65],"matrices.":[67],"also":[69],"provide":[70],"estimates":[71],"how":[73],"close":[74],"constructed":[76],"are":[78],"known":[81],"did":[85],"not":[86],"previously":[87],"have":[88],"asymptotic":[89],"estimates.":[90]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}