{"id":"https://openalex.org/W7204889406","doi":"https://doi.org/10.3390/math14213904","title":"On Topological Numerical Transitivity, C*-Transitivity, and Generalized Numerical Transitivity","display_name":"On Topological Numerical Transitivity, C*-Transitivity, and Generalized Numerical Transitivity","publication_year":2026,"publication_date":"2026-10-26","ids":{"openalex":"https://openalex.org/W7204889406","doi":"https://doi.org/10.3390/math14213904"},"language":"en","primary_location":{"id":"doi:10.3390/math14213904","doi":"https://doi.org/10.3390/math14213904","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14213904","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/math14213904","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005501439","display_name":"Otmane Benchiheb","orcid":"https://orcid.org/0000-0002-6759-2368","observed_orcids":["https://orcid.org/0000-0002-6759-2368"]},"institutions":[{"id":"https://openalex.org/I4210125507","display_name":"Chouaib Doukkali University","ror":"https://ror.org/036kgyt43","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210125507"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Otmane Benchiheb","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, El Jadida 24000, Morocco"],"raw_orcid":"https://orcid.org/0000-0002-6759-2368","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, El Jadida 24000, Morocco","institution_ids":["https://openalex.org/I4210125507"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062112961","display_name":"Stefan Ivkovi\u0107","orcid":"https://orcid.org/0000-0003-2248-8206","observed_orcids":["https://orcid.org/0000-0003-2248-8206"]},"institutions":[{"id":"https://openalex.org/I4390039372","display_name":"Mathematical Institute of the Serbian Academy of Sciences and Arts","ror":"https://ror.org/02jxk1021","country_code":"RS","type":"education","lineage":["https://openalex.org/I1338511612","https://openalex.org/I4390039372"]}],"countries":["RS"],"is_corresponding":true,"raw_author_name":"Stefan Ivkovi\u0107","raw_affiliation_strings":["Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia"],"raw_orcid":"https://orcid.org/0000-0003-2248-8206","affiliations":[{"raw_affiliation_string":"Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia","institution_ids":["https://openalex.org/I4390039372"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062112961"],"corresponding_institution_ids":["https://openalex.org/I4390039372"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.57471313,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"21","first_page":"3904","last_page":"3904"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.9854000210762024,"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"}},"topics":[{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.9854000210762024,"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":0.007300000172108412,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.001500000013038516,"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/linear-dynamics","display_name":"linear dynamics","score":0.7540000081062317},{"id":"https://openalex.org/keywords/banach-algebras","display_name":"Banach algebras","score":0.8949999809265137},{"id":"https://openalex.org/keywords/hilbert-schmidt-operators","display_name":"Hilbert-Schmidt operators","score":0.9340000152587891},{"id":"https://openalex.org/keywords/compact-operators","display_name":"compact operators","score":0.6690000295639038},{"id":"https://openalex.org/keywords/hilbert-c-modules","display_name":"Hilbert C*-modules","score":0.8999999761581421},{"id":"https://openalex.org/keywords/diagonal-operators","display_name":"diagonal operators","score":0.9800000190734863},{"id":"https://openalex.org/keywords/supercyclicity","display_name":"supercyclicity","score":0.8460000157356262}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.849399983882904},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.7641000151634216},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7124999761581421},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.6310999989509583},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.5519000291824341},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.5432000160217285},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5060999989509583},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.43369999527931213},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4065999984741211},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35359999537467957},{"id":"https://openalex.org/C174058634","wikidata":"https://www.wikidata.org/wiki/Q5155314","display_name":"Compact operator on Hilbert space","level":4,"score":0.3465000092983246},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C152306953","wikidata":"https://www.wikidata.org/wiki/Q621744","display_name":"Approximation property","level":3,"score":0.30230000615119934},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/math14213904","doi":"https://doi.org/10.3390/math14213904","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14213904","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2608.29436","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29436","pdf_url":"https://arxiv.org/pdf/2608.29436","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.2608.29436","doi":"https://doi.org/10.48550/arxiv.2608.29436","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29436","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":"doi:10.3390/math14213904","doi":"https://doi.org/10.3390/math14213904","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14213904","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204889406.pdf","grobid_xml":"https://content.openalex.org/works/W7204889406.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W409772452","https://openalex.org/W626893493","https://openalex.org/W1486267208","https://openalex.org/W1549649164","https://openalex.org/W1650352370","https://openalex.org/W1657944681","https://openalex.org/W1967015748","https://openalex.org/W1980494725","https://openalex.org/W1984606426","https://openalex.org/W1990183213","https://openalex.org/W1991137003","https://openalex.org/W1992908827","https://openalex.org/W1995638525","https://openalex.org/W2005864902","https://openalex.org/W2009672041","https://openalex.org/W2021471696","https://openalex.org/W2053241748","https://openalex.org/W2055988993","https://openalex.org/W2066058640","https://openalex.org/W2073540558","https://openalex.org/W2074515870","https://openalex.org/W2091399356","https://openalex.org/W2168966995","https://openalex.org/W2218360103","https://openalex.org/W2768077255","https://openalex.org/W3037567748","https://openalex.org/W3159573928","https://openalex.org/W3195910145","https://openalex.org/W4240509971","https://openalex.org/W4255815477","https://openalex.org/W4412757466","https://openalex.org/W4417145624","https://openalex.org/W7160896779","https://openalex.org/W7165741085"],"related_works":["https://openalex.org/W3010557133","https://openalex.org/W2060307825","https://openalex.org/W4414806819","https://openalex.org/W2014198867","https://openalex.org/W7141120674","https://openalex.org/W2992621208","https://openalex.org/W3183621648","https://openalex.org/W2168570640","https://openalex.org/W2218360103","https://openalex.org/W1624279039"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"the":[2,38,44,61,83,107,153,169,250,264,267,319,330],"concept":[3,52],"of":[4,46,53,63,112,130,155,192,202,208,229,266,293,321,329],"numerical":[5,19,22,92,98,101,194,198,215,218,272],"hypercyclicity,":[6,89,102,219,297],"in":[7,15,43,86,106,200,280,313],"this":[8,209,259],"paper":[9],"we":[10,76,104,109,143,175,188,211,241,269,302,316,325],"introduce":[11,318],"three":[12],"new":[13,70],"notions":[14,71,85,279],"linear":[16,281],"dynamics:":[17],"topological":[18,97,197,271],"transitivity,":[20,23,323],"generalized":[21,139,148],"and":[24,75,91,115,147,183,187,196,216,257,274,298,301,324],"C\u2217-transitivity.":[25],"The":[26,51],"first":[27],"notion":[28,320],"is":[29,55],"defined":[30],"for":[31,246,336],"operators":[32,47,59,119,133,151,157,167,178,248],"on":[33,48,60,152,158,168,179,184,223,249,332],"general":[34],"Banach":[35,49],"spaces,":[36],"whereas":[37],"latter":[39],"two":[40,233],"are":[41,72,121,135],"formulated":[42],"setting":[45],"algebras.":[50],"C\u2217-transitivity":[54,275,333],"also":[56,77,127,317],"applicable":[57],"to":[58,254],"space":[62,228],"Hilbert\u2013Schmidt":[64],"operators.":[65],"We":[66,126],"prove":[67,212,303],"that":[68,79,120,134,304,327],"these":[69,310],"mutually":[73],"different,":[74],"show":[78],"they":[80,305],"differ":[81,307],"from":[82,308],"standard":[84,170,251,278,311],"dynamics":[87],"like":[88,283],"supercyclicity,":[90,285,287,300],"hypercyclicity.":[93],"In":[94,173],"particular,":[95],"while":[96],"transitivity":[99,199,273],"implies":[100],"as":[103,163,165],"argue":[105,326],"paper,":[108,268],"provide":[110,128,242],"examples":[111,129],"numerically":[113,117,124,131,140,149,238],"hypercyclic":[114,118,132],"strongly":[116],"not":[122],"topologically":[123,237],"transitive.":[125,141,239],"neither":[136],"C\u2217-transitive":[137,146,166],"nor":[138],"Also,":[142],"construct":[144],"nonsupercyclic":[145],"transitive":[150],"C\u2217-algebra":[154],"compact":[156],"a":[159,206,220,224],"separable":[160],"Hilbert":[161,171,181,227,252],"space,":[162],"well":[164],"C\u2217-module.":[172],"addition,":[174],"study":[176],"diagonal":[177,221,247],"finite-dimensional":[180,225],"spaces":[182],"\u2113p(N),":[185],"1<p<\u221e,":[186],"obtain":[189],"complete":[190],"characterizations":[191],"both":[193],"hypercyclicity":[195],"terms":[201],"coefficient-simplex":[203],"criteria.":[204],"As":[205],"consequence":[207],"result,":[210],"that,":[213],"unlike":[214],"strong":[217],"operator":[222],"complex":[226],"dimension":[230],"at":[231],"least":[232],"can":[234],"never":[235],"be":[236,255],"Furthermore,":[240],"some":[243],"sufficient":[244],"conditions":[245],"C\u2217-module":[253],"C\u2217-transitive,":[256],"illustrate":[258],"result":[260],"with":[261,276],"examples.":[262],"At":[263],"end":[265],"compare":[270],"numerous":[277],"dynamics,":[282],"N-weak":[284],"weak-n":[286],"\u03f5\u2013cyclicity,":[288],"Li\u2013Yorke":[289],"chaos,":[290],"distributional":[291],"chaos":[292],"type":[294],"3,":[295],"subspace":[296,299],"genuinely":[306],"all":[309],"concepts":[312],"dynamics.":[314],"Finally,":[315],"C\u2217-numerical":[322,337],"many":[328],"results":[331],"hold":[334],"analogously":[335],"transitivity.":[338]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-02T00:00:00"}
