{"id":"https://openalex.org/W7203744087","doi":"https://doi.org/10.31392/mfat-npu26_2.2026.04","title":"The dual of ( p , \u03c3 ) -weakly summable sequences space and its application","display_name":"The dual of ( p , \u03c3 ) -weakly summable sequences space and its application","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7203744087","doi":"https://doi.org/10.31392/mfat-npu26_2.2026.04"},"language":"en","primary_location":{"id":"doi:10.31392/mfat-npu26_2.2026.04","doi":"https://doi.org/10.31392/mfat-npu26_2.2026.04","is_oa":true,"landing_page_url":"https://doi.org/10.31392/mfat-npu26_2.2026.04","pdf_url":"https://mfat.imath.kiev.ua/article/2026/02/mfat_2026_02_2279.pdf","source":{"id":"https://openalex.org/S2737028565","display_name":"Methods of Functional Analysis and Topology","issn_l":"1029-3531","issn":["1029-3531","2415-7503"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1","poland-40","russia-white-list-4"],"host_organization":"https://openalex.org/P4310322009","host_organization_name":"Institute of Mathematics of the National Academy of Sciences of Ukraine","host_organization_lineage":["https://openalex.org/P4310322009","https://openalex.org/P4310321802"],"host_organization_lineage_names":["Institute of Mathematics of the National Academy of Sciences of Ukraine","National Academy of Sciences of Ukraine"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Methods of Functional Analysis and Topology","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://mfat.imath.kiev.ua/article/2026/02/mfat_2026_02_2279.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049592345","display_name":"Athmane Ferradi","orcid":"https://orcid.org/0000-0002-3622-2508","observed_orcids":["https://orcid.org/0000-0002-3622-2508"]},"institutions":[{"id":"https://openalex.org/I4405253935","display_name":"\u00c9cole Normale Sup\u00e9rieure de Bou Saada","ror":"https://ror.org/017kx4966","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4405253935"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Ferradi Athmane","raw_affiliation_strings":["Department of Mathematics , Ecole Normale Sup\u00e9rieure de Bousaada , 28001 Bou Saada , Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Ecole Normale Sup\u00e9rieure de Bousaada , 28001 Bou Saada , Algeria","institution_ids":["https://openalex.org/I4405253935"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049592345"],"corresponding_institution_ids":["https://openalex.org/I4405253935"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":"2","first_page":"139","last_page":"151"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.7505000233650208,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.7505000233650208,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.24459999799728394,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.0005000000237487257,"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/dual-spaces","display_name":"dual spaces","score":0.6209999918937683},{"id":"https://openalex.org/keywords/topological-dual","display_name":"topological dual","score":0.8199999928474426},{"id":"https://openalex.org/keywords/adjoint-operators","display_name":"adjoint operators","score":0.8560000061988831},{"id":"https://openalex.org/keywords/sequence-spaces","display_name":"sequence spaces","score":0.36800000071525574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7534000277519226},{"id":"https://openalex.org/C45633534","wikidata":"https://www.wikidata.org/wiki/Q752487","display_name":"Dual space","level":2,"score":0.6815999746322632},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6460999846458435},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.6413999795913696},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47589999437332153},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.41830000281333923},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.41530001163482666},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39100000262260437},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.38269999623298645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35740000009536743},{"id":"https://openalex.org/C30711495","wikidata":"https://www.wikidata.org/wiki/Q289411","display_name":"Sequence space","level":3,"score":0.32899999618530273},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C84750791","wikidata":"https://www.wikidata.org/wiki/Q3427408","display_name":"Dual representation","level":3,"score":0.2897000014781952},{"id":"https://openalex.org/C198586994","wikidata":"https://www.wikidata.org/wiki/Q96376663","display_name":"Dual pair","level":5,"score":0.2720000147819519}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.31392/mfat-npu26_2.2026.04","doi":"https://doi.org/10.31392/mfat-npu26_2.2026.04","is_oa":true,"landing_page_url":"https://doi.org/10.31392/mfat-npu26_2.2026.04","pdf_url":"https://mfat.imath.kiev.ua/article/2026/02/mfat_2026_02_2279.pdf","source":{"id":"https://openalex.org/S2737028565","display_name":"Methods of Functional Analysis and Topology","issn_l":"1029-3531","issn":["1029-3531","2415-7503"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1","poland-40","russia-white-list-4"],"host_organization":"https://openalex.org/P4310322009","host_organization_name":"Institute of Mathematics of the National Academy of Sciences of Ukraine","host_organization_lineage":["https://openalex.org/P4310322009","https://openalex.org/P4310321802"],"host_organization_lineage_names":["Institute of Mathematics of the National Academy of Sciences of Ukraine","National Academy of Sciences of Ukraine"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Methods of Functional Analysis and Topology","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.31392/mfat-npu26_2.2026.04","doi":"https://doi.org/10.31392/mfat-npu26_2.2026.04","is_oa":true,"landing_page_url":"https://doi.org/10.31392/mfat-npu26_2.2026.04","pdf_url":"https://mfat.imath.kiev.ua/article/2026/02/mfat_2026_02_2279.pdf","source":{"id":"https://openalex.org/S2737028565","display_name":"Methods of Functional Analysis and Topology","issn_l":"1029-3531","issn":["1029-3531","2415-7503"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1","poland-40","russia-white-list-4"],"host_organization":"https://openalex.org/P4310322009","host_organization_name":"Institute of Mathematics of the National Academy of Sciences of Ukraine","host_organization_lineage":["https://openalex.org/P4310322009","https://openalex.org/P4310321802"],"host_organization_lineage_names":["Institute of Mathematics of the National Academy of Sciences of Ukraine","National Academy of Sciences of Ukraine"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Methods of Functional Analysis and Topology","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335007","display_name":"Direction G\u00e9n\u00e9rale de la Recherche Scientifique et du D\u00e9veloppement Technologique","ror":"https://ror.org/04jpfrv51"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203744087.pdf","grobid_xml":"https://content.openalex.org/works/W7203744087.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1978220858","https://openalex.org/W1997317886","https://openalex.org/W2030562014","https://openalex.org/W2042116330","https://openalex.org/W2042708818","https://openalex.org/W2135659771","https://openalex.org/W3007338849","https://openalex.org/W3132407661","https://openalex.org/W3189574036","https://openalex.org/W4313569224"],"related_works":["https://openalex.org/W3146768656","https://openalex.org/W2792358665","https://openalex.org/W2591767206","https://openalex.org/W814761606","https://openalex.org/W4399434986","https://openalex.org/W1997571474","https://openalex.org/W6979713066","https://openalex.org/W2087765362","https://openalex.org/W7095283115","https://openalex.org/W1590540253"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,29],"prove":[4],"that":[5,34],"the":[6,15,19],"space":[7,20],"of":[8,18,21],"strongly":[9,60],"\\((r,":[10],"p,":[11],"\\sigma)\\)-summable":[12],"sequences":[13],"is":[14,43,59],"topological":[16],"dual":[17],"\\((p,":[22,44],"\\sigma)\\)-weakly":[23],"summable":[24],"sequences.":[25],"As":[26],"an":[27,35],"application,":[28],"provide":[30],"a":[31],"new":[32],"proof":[33],"operator":[36],"\\(":[37,53],"T:":[38],"E":[39],"\\to":[40,56],"F":[41],"\\)":[42,58],"\\sigma)\\)-absolutely":[45],"continuous":[46],"if":[47,50],"and":[48],"only":[49],"its":[51],"adjoint":[52],"T^*:":[54],"F^*":[55],"E^*":[57],"\\((p^*,":[61],"\\sigma)\\)-continuous.":[62]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-08-20T00:00:00"}