{"id":"https://openalex.org/W7212286258","doi":"https://doi.org/10.48550/arxiv.2609.10957","title":"Typical dynamical properties of operators on $\\ell_p$","display_name":"Typical dynamical properties of operators on $\\ell_p$","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212286258","doi":"https://doi.org/10.48550/arxiv.2609.10957"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.10957","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10957","pdf_url":"https://arxiv.org/pdf/2609.10957","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.10957","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151383064","display_name":"Jian Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I32574673","display_name":"Shantou University","ror":"https://ror.org/01a099706","country_code":"CN","type":"education","lineage":["https://openalex.org/I32574673"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Jian","raw_affiliation_strings":["Institute for Mathematical Sciences and Artificial Intelligence & Department of Mathematics , Shantou University , Shantou , 515821 , Guangdong , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematical Sciences and Artificial Intelligence & Department of Mathematics , Shantou University , Shantou , 515821 , Guangdong , China","institution_ids":["https://openalex.org/I32574673"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101335477","display_name":"Qijing Liao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I32574673","display_name":"Shantou University","ror":"https://ror.org/01a099706","country_code":"CN","type":"education","lineage":["https://openalex.org/I32574673"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liao, Qijing","raw_affiliation_strings":["Department of Mathematics , Shantou University , Shantou , 515821 , Guangdong , China","Institute for Mathematical Sciences and Artificial Intelligence & Department of Mathematics , Shantou University , Shantou , 515821 , Guangdong , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Shantou University , Shantou , 515821 , Guangdong , China","institution_ids":["https://openalex.org/I32574673"]},{"raw_affiliation_string":"Institute for Mathematical Sciences and Artificial Intelligence & Department of Mathematics , Shantou University , Shantou , 515821 , Guangdong , China","institution_ids":["https://openalex.org/I32574673"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I32574673"],"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9179999828338623,"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":0.9179999828338623,"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":0.054099999368190765,"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":0.01759999990463257,"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/hypercyclic-operators","display_name":"hypercyclic operators","score":0.9620000123977661},{"id":"https://openalex.org/keywords/lp-spaces","display_name":"Lp spaces","score":0.6159999966621399},{"id":"https://openalex.org/keywords/bounded-linear-operators","display_name":"bounded linear operators","score":0.6819999814033508},{"id":"https://openalex.org/keywords/operator-dynamics","display_name":"operator dynamics","score":0.3100000023841858}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.8727999925613403},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7251999974250793},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6653000116348267},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5996999740600586},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.5821999907493591},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5001000165939331},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4648999869823456},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4643999934196472},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.460099995136261},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4481000006198883},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.420199990272522},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.3986999988555908},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.3952000141143799},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3831000030040741},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.3709999918937683},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.359499990940094},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2563000023365021},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.10957","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10957","pdf_url":"https://arxiv.org/pdf/2609.10957","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.2609.10957","doi":"https://doi.org/10.48550/arxiv.2609.10957","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.10957","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:2609.10957","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10957","pdf_url":"https://arxiv.org/pdf/2609.10957","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/G239404273","display_name":null,"funder_award_id":"12222110","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212286258.pdf","grobid_xml":"https://content.openalex.org/works/W7212286258.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1650352370","https://openalex.org/W1968584349","https://openalex.org/W4389422220","https://openalex.org/W4405425561","https://openalex.org/W4409198617","https://openalex.org/W1566878868","https://openalex.org/W7114769642","https://openalex.org/W3129272755","https://openalex.org/W2071542267","https://openalex.org/W3184256712"],"abstract_inverted_index":{"We":[0,30,68],"investigate":[1],"the":[2,11,72,78,87],"typical":[3,38,74],"dynamical":[4,75],"properties":[5,76],"of":[6,13],"hypercyclic":[7,51,63],"operators":[8,17],"in":[9],"$\\mathcal{L}_M(X)$,":[10],"set":[12],"all":[14],"bounded":[15],"linear":[16],"on":[18],"$X$":[19],"whose":[20],"norms":[21],"are":[22],"at":[23],"most":[24],"$M$,":[25],"when":[26],"$X=\\ell_p$,":[27],"$1<":[28],"p<\\infty$.":[29],"show":[31,70],"that,":[32],"with":[33,86],"respect":[34],"to":[35],"SOT$^*$,":[36],"a":[37,49,93],"operator":[39,52],"$T\\in":[40],"\\mathcal{L}_M(X)$":[41],"is":[42,45,54,61,92],"weakly":[43,46],"mixing,":[44],"disjoint":[47,62],"from":[48],"given":[50],"$S$,":[53],"not":[55],"topologically":[56],"ergodic,":[57],"and":[58],"satisfies":[59],"$(T,T^2,\\dotsc,T^k)$":[60],"for":[64,77],"any":[65],"$k\\geq":[66],"2$.":[67],"also":[69],"that":[71],"similar":[73],"concrete":[79],"family":[80],"$\\mathcal{M}=\\{I+B_w\\in":[81],"\\mathcal{L}(X)\\colon":[82],"w\\in":[83],"c_0(\\mathbb{Z})\\}$,":[84],"endowed":[85],"norm":[88],"topology,":[89],"where":[90],"$B_w$":[91],"bilateral":[94],"weighted":[95],"backward":[96],"shift.":[97]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-12T00:00:00"}