{"id":"https://openalex.org/W7215128167","doi":"https://doi.org/10.48550/arxiv.2609.40189","title":"Convergence of spectral smoothings from compact quantum group actions","display_name":"Convergence of spectral smoothings from compact quantum group actions","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7215128167","doi":"https://doi.org/10.48550/arxiv.2609.40189"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.40189","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.40189","pdf_url":"https://arxiv.org/pdf/2609.40189","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/2609.40189","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115002496","display_name":"Trevor R Camper","orcid":"https://orcid.org/0000-0002-6966-3916","observed_orcids":["https://orcid.org/0000-0002-6966-3916"]},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Camper, Trevor","raw_affiliation_strings":["Department of Mathematics , Dartmouth College , 337 Kemeny Hall , Hanover , NH 03755 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Dartmouth College , 337 Kemeny Hall , Hanover , NH 03755 , USA","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076538541","display_name":"Dimitrios Giannakis","orcid":"https://orcid.org/0000-0002-4220-0313","observed_orcids":["https://orcid.org/0000-0002-4220-0313"]},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Giannakis, Dimitrios","raw_affiliation_strings":["Department of Mathematics , Dartmouth College , 314 Kemeny Hall , Hanover , NH 03755 , USA","Department of Mathematics , Dartmouth College , 337 Kemeny Hall , Hanover , NH 03755 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Dartmouth College , 314 Kemeny Hall , Hanover , NH 03755 , USA","institution_ids":["https://openalex.org/I107672454"]},{"raw_affiliation_string":"Department of Mathematics , Dartmouth College , 337 Kemeny Hall , Hanover , NH 03755 , USA","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088772197","display_name":"Gage Hoefer","orcid":"https://orcid.org/0000-0001-7481-6166","observed_orcids":["https://orcid.org/0000-0001-7481-6166"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hoefer, Gage","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9994999766349792,"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":0.9994999766349792,"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/T11545","display_name":"Advanced Banach Space Theory","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"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0,"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/compact-quantum-groups","display_name":"compact quantum groups","score":0.906000018119812},{"id":"https://openalex.org/keywords/operator-systems","display_name":"operator systems","score":0.7300000190734863},{"id":"https://openalex.org/keywords/c-algebras","display_name":"C*-algebras","score":0.8960000276565552},{"id":"https://openalex.org/keywords/quantum-metric","display_name":"quantum metric","score":0.8949999809265137},{"id":"https://openalex.org/keywords/bounded-approximate-identity","display_name":"bounded approximate identity","score":0.7689999938011169},{"id":"https://openalex.org/keywords/spectral-truncation","display_name":"spectral truncation","score":0.7490000128746033},{"id":"https://openalex.org/keywords/compact-galaxy-groups","display_name":"compact groups","score":0.7889999747276306}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7014999985694885},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6313999891281128},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5634999871253967},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5382999777793884},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5066999793052673},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5041000247001648},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5008000135421753},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4796999990940094},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4796999990940094},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4611999988555908},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C116827671","wikidata":"https://www.wikidata.org/wiki/Q5155316","display_name":"Compact quantum group","level":4,"score":0.3905999958515167},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.38920000195503235},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.37059998512268066},{"id":"https://openalex.org/C130133044","wikidata":"https://www.wikidata.org/wiki/Q1887083","display_name":"Compact group","level":3,"score":0.34360000491142273},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.3160000145435333},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.2685000002384186},{"id":"https://openalex.org/C49976459","wikidata":"https://www.wikidata.org/wiki/Q17103517","display_name":"Spectral triple","level":4,"score":0.2662999927997589},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.2606000006198883},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.2590000033378601},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.2583000063896179},{"id":"https://openalex.org/C186123792","wikidata":"https://www.wikidata.org/wiki/Q7390277","display_name":"SIC-POVM","level":5,"score":0.2565000057220459}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.40189","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.40189","pdf_url":"https://arxiv.org/pdf/2609.40189","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.2609.40189","doi":"https://doi.org/10.48550/arxiv.2609.40189","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.40189","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:2609.40189","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.40189","pdf_url":"https://arxiv.org/pdf/2609.40189","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/G168130044","display_name":"Institut Mittag-Leffler","funder_award_id":"2021-06594","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"}],"funders":[{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7215128167.pdf","grobid_xml":"https://content.openalex.org/works/W7215128167.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2152810766","https://openalex.org/W4387075172","https://openalex.org/W4416740858"],"related_works":["https://openalex.org/W4384522658","https://openalex.org/W4416740858","https://openalex.org/W7159680758","https://openalex.org/W4416783685","https://openalex.org/W4387075172","https://openalex.org/W7167689055","https://openalex.org/W2352303497","https://openalex.org/W2034487574","https://openalex.org/W2744630797","https://openalex.org/W2064084516"],"abstract_inverted_index":{"In":[0],"this":[1],"note,":[2],"we":[3,34],"study":[4],"complete":[5,75],"and":[6,50,76,95],"quantum":[7,28,43,56,77],"Gromov-Hausdorff":[8,78],"convergence":[9,88],"of":[10,16,25,68,89,92],"operator":[11],"systems":[12],"obtained":[13],"using":[14],"smoothings":[15,20],"C*-algebras,":[17],"where":[18],"our":[19],"arise":[21],"from":[22],"the":[23,31,69,74,87],"action":[24],"a":[26,40],"compact":[27,42,93],"group":[29,44],"on":[30,46],"C*-algebra.":[32],"Specifically,":[33],"show":[35],"how":[36],"if":[37],"$\\mathbb{G}$":[38],"is":[39],"co-amenable":[41],"acting":[45],"unital":[47],"C*-algebra":[48],"$\\mathcal{A}$,":[49],"both":[51],"are":[52],"equipped":[53],"with":[54],"suitable":[55],"metrics,":[57],"bounded":[58],"approximate":[59],"identities":[60],"in":[61],"$L^{1}(\\mathbb{G})$":[62],"may":[63],"be":[64],"used":[65],"for":[66],"approximations":[67],"original":[70],"space":[71],"$\\mathcal{A}$":[72],"under":[73],"distance.":[79],"We":[80],"finish":[81],"by":[82],"presenting":[83],"some":[84],"applications":[85],"to":[86,97],"spectral":[90],"truncations":[91],"groups":[94],"connections":[96],"previous":[98],"results.":[99]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-02T00:00:00"}