{"id":"https://openalex.org/W7223787474","doi":"https://doi.org/10.48550/arxiv.2610.35644","title":"Relative norm averaging property and selflessness of almost periodic actions","display_name":"Relative norm averaging property and selflessness of almost periodic actions","publication_year":2026,"publication_date":"2026-10-26","ids":{"openalex":"https://openalex.org/W7223787474","doi":"https://doi.org/10.48550/arxiv.2610.35644"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.35644","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.35644","pdf_url":"https://arxiv.org/pdf/2610.35644","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/2610.35644","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019817297","display_name":"Ryo Toyota","orcid":"https://orcid.org/0009-0001-8282-012X","observed_orcids":["https://orcid.org/0009-0001-8282-012X"]},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Toyota, Ryo","raw_affiliation_strings":["Department of Mathematical Sciences , University of Copenhagen , Universitetsparken 5 , DK- 2100 , Copenhagen \u00d8 , Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , University of Copenhagen , Universitetsparken 5 , DK- 2100 , Copenhagen \u00d8 , Denmark","institution_ids":["https://openalex.org/I124055696"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019817297"],"corresponding_institution_ids":["https://openalex.org/I124055696"],"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/T10884","display_name":"Holomorphic and Operator Theory","score":9.999999747378752e-05,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/discrete-groups","display_name":"discrete groups","score":0.6940000057220459},{"id":"https://openalex.org/keywords/faithful-states","display_name":"faithful states","score":0.453000009059906},{"id":"https://openalex.org/keywords/relative-commutant","display_name":"relative commutant","score":0.5370000004768372},{"id":"https://openalex.org/keywords/reduced-group-c-algebras","display_name":"reduced group C*-algebras","score":0.6159999966621399},{"id":"https://openalex.org/keywords/ergodic-actions","display_name":"ergodic actions","score":0.6899999976158142},{"id":"https://openalex.org/keywords/free-group-on-two-generators","display_name":"free group on two generators","score":0.8640000224113464}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7997999787330627},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.675599992275238},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.6272000074386597},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6245999932289124},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.5221999883651733},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5102999806404114},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4275999963283539},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3869999945163727},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3605000078678131},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3517000079154968},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.265500009059906}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.35644","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.35644","pdf_url":"https://arxiv.org/pdf/2610.35644","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.2610.35644","doi":"https://doi.org/10.48550/arxiv.2610.35644","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.35644","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:2610.35644","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.35644","pdf_url":"https://arxiv.org/pdf/2610.35644","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223787474.pdf","grobid_xml":"https://content.openalex.org/works/W7223787474.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7204553651","https://openalex.org/W7214768336","https://openalex.org/W2085849170","https://openalex.org/W2053404138","https://openalex.org/W2075763735","https://openalex.org/W7223654955","https://openalex.org/W592126010","https://openalex.org/W7098091831","https://openalex.org/W2950316294","https://openalex.org/W2907003981"],"abstract_inverted_index":{"Let":[0],"$D$":[1],"be":[2,14],"a":[3,8,15,20],"unital":[4],"separable":[5],"$C^*$-algebra":[6],"with":[7,85],"faithful":[9],"state":[10],"$\u03c3$":[11],"and":[12,54,73],"$G$":[13,34,67,125],"discrete":[16],"group.":[17],"We":[18,37],"introduce":[19],"property":[21,26,69,115],"called":[22],"relative":[23,112],"norm":[24,113],"averaging":[25,114],"(RNA)":[27],"for":[28],"almost":[29,42,81],"periodic":[30,43,82],"$\u03c3$-preserving":[31,44,83],"actions":[32,99],"by":[33],"on":[35,102],"$(D,\u03c3)$.":[36],"prove":[38,64,109],"that":[39,48,65,110,117],"if":[40,66,124],"an":[41,61,77],"action":[45,84],"$\u03b1$":[46,57],"satisfies":[47,58,120,126],"$\\overline{\u03b1(G)}":[49],"\\subseteq":[50],"\\text{Aut}(D,\u03c3)$":[51],"is":[52,76,92],"connected":[53],"nontrivial,":[55],"then":[56,89],"(RNA).":[59],"As":[60],"application,":[62],"we":[63,108],"has":[68],"PHP":[70],"of":[71,100],"Ozawa":[72],"$\u03b1:G\\curvearrowright":[74],"(D,\u03c3)$":[75],"ergodic":[78],"(i.e.":[79],"$D^G=\\mathbb{C}$)":[80],"$\\overline{\u03b1(G)}$":[86],"being":[87],"connected,":[88],"$D\\rtimes_r":[90,118],"G$":[91,119],"selfless.":[93],"This":[94],"includes":[95],"certain":[96],"paradoxical":[97],"isometric":[98],"$\\mathbb{F}_2$":[101],"the":[103,111,121],"sphere.":[104],"In":[105],"non-ergodic":[106],"case,":[107],"implies":[116],"$D^G$-valued":[122],"selfless,":[123],"PHP.":[127]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-28T00:00:00"}