{"id":"https://openalex.org/W7203919348","doi":"https://doi.org/10.48550/arxiv.2608.18125","title":"Putnam-Fuglede commutativity and the range-kernel orthogonality of an elementary operator","display_name":"Putnam-Fuglede commutativity and the range-kernel orthogonality of an elementary operator","publication_year":2026,"publication_date":"2026-07-20","ids":{"openalex":"https://openalex.org/W7203919348","doi":"https://doi.org/10.48550/arxiv.2608.18125"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.18125","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.18125","pdf_url":"https://arxiv.org/pdf/2608.18125","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/2608.18125","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115513597","display_name":"Mohamed Morjane","orcid":"https://orcid.org/0009-0004-8440-6557","observed_orcids":["https://orcid.org/0009-0004-8440-6557"]},"institutions":[{"id":"https://openalex.org/I3121676899","display_name":"Universit\u00e9 Ibn-Tofail","ror":"https://ror.org/02wj89n04","country_code":"MA","type":"education","lineage":["https://openalex.org/I3121676899"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Morjane, M.","raw_affiliation_strings":["Faculty of Science , Ibn Tofail University , P.O. Box 133 , K\u00e9nitra , Morocco","Laboratory of Analysis, Geometry and Applications , Department of Mathematics ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science , Ibn Tofail University , P.O. Box 133 , K\u00e9nitra , Morocco","institution_ids":["https://openalex.org/I3121676899"]},{"raw_affiliation_string":"Laboratory of Analysis, Geometry and Applications , Department of Mathematics ,","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082339020","display_name":"Mohamed Ech-Chad","orcid":"https://orcid.org/0000-0003-3688-9019","observed_orcids":["https://orcid.org/0000-0003-3688-9019"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ech-chad, M.","raw_affiliation_strings":["Laboratory of Analysis, Geometry and Applications , Department of Mathematics ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Analysis, Geometry and Applications , Department of Mathematics ,","institution_ids":[]}]}],"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.8237000107765198,"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":0.8237000107765198,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.1492999941110611,"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":0.013700000010430813,"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/elementary-operators","display_name":"elementary operators","score":0.8799999952316284},{"id":"https://openalex.org/keywords/normal-operators","display_name":"normal operators","score":0.9210000038146973},{"id":"https://openalex.org/keywords/commuting-operators","display_name":"commuting operators","score":0.7329999804496765},{"id":"https://openalex.org/keywords/operator-algebras","display_name":"operator algebras","score":0.5870000123977661},{"id":"https://openalex.org/keywords/commutator-operators","display_name":"commutator operators","score":0.49399998784065247}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7720000147819519},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.6949999928474426},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.6559000015258789},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6341000199317932},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5981000065803528},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5559999942779541},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4611000120639801},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4131999909877777},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.4088999927043915},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.38359999656677246},{"id":"https://openalex.org/C2992500303","wikidata":"https://www.wikidata.org/wiki/Q5680845","display_name":"Operator matrix","level":2,"score":0.3720000088214874},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36629998683929443},{"id":"https://openalex.org/C24250787","wikidata":"https://www.wikidata.org/wiki/Q7269510","display_name":"Quasinormal operator","level":4,"score":0.33869999647140503},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.33730000257492065},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.33570000529289246},{"id":"https://openalex.org/C176691602","wikidata":"https://www.wikidata.org/wiki/Q7097841","display_name":"Operator space","level":4,"score":0.33169999718666077},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.31619998812675476},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.310699999332428},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.3084999918937683},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C149016480","wikidata":"https://www.wikidata.org/wiki/Q3277121","display_name":"Weak operator topology","level":5,"score":0.303600013256073},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29809999465942383},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C65630602","wikidata":"https://www.wikidata.org/wiki/Q2278680","display_name":"Shift operator","level":4,"score":0.2808000147342682},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.27489998936653137}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.18125","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.18125","pdf_url":"https://arxiv.org/pdf/2608.18125","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.2608.18125","doi":"https://doi.org/10.48550/arxiv.2608.18125","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.18125","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:2608.18125","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.18125","pdf_url":"https://arxiv.org/pdf/2608.18125","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/W7203919348.pdf","grobid_xml":"https://content.openalex.org/works/W7203919348.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7214224189","https://openalex.org/W4404765884","https://openalex.org/W7223177189","https://openalex.org/W2127101376","https://openalex.org/W1531633510","https://openalex.org/W1984076505","https://openalex.org/W2021953810","https://openalex.org/W2598293766","https://openalex.org/W1972958938","https://openalex.org/W4206805074"],"abstract_inverted_index":{"Given":[0],"Hilbert":[1],"space":[2],"commuting":[3],"operators":[4],"$T,":[5],"S":[6],"\\in":[7,28],"\\mcl(H)$,":[8],"such":[9],"that":[10,51],"$T$":[11],"is":[12,22,66],"$w$-hyponormal":[13],"with":[14],"$\\ker":[15,53,88],"T":[16,40,89],"\\subseteq":[17],"\\ker":[18,57,79,91],"T^*$":[19],"and":[20,85],"$S$":[21],"normal":[23],"operator.":[24],"Let":[25],"$\u03d5_{T,":[26,36,64,72],"S}":[27,37,55,81],"\\mcl(\\mcl(H))$":[29,104],"be":[30],"the":[31,69,100,121],"elementary":[32,101,122],"operator":[33,102,123],"defined":[34,105],"by":[35,106],"(X)":[38],"=":[39],"X":[41,43,108,110],"S^*-S":[42],"T^*$.":[44],"In":[45],"this":[46],"paper,":[47],"we":[48,94],"show":[49],"firstly":[50],"(1)":[52],"\u03d5_{T,":[54,80],"\\subset":[56],"\u03d5_{T^*,":[58],"S^*}$.":[59],"(2)":[60],"The":[61],"range":[62],"of":[63,71],"S}$":[65,73],"orthogonal":[67],"to":[68,99],"kernel":[70],"(":[74],"$":[75,82],"\\mcr(\u03d5_{T,":[76],"S})":[77],"\\perp":[78],")":[83],"if":[84,87],"only":[86],"\\cap":[90],"S=\\{0\\}$.":[92],"Secondly,":[93],"will":[95],"extend":[96],"these":[97],"results":[98,119],"$\u03a6\\in":[103],"$\\;\u03a6(X)=A":[107],"D-C":[109],"B$":[111],"where":[112],"$[A,":[113],"C]=[B,":[114],"D]=":[115],"0$.":[116],"Related":[117],"orthogonality":[118],"for":[120],"$\u03a6$":[124],"are":[125],"also":[126],"given.":[127]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-22T00:00:00"}