{"doi":"10.5802/ambp.203","title":"Towards a theory of some unbounded linear operators on\n                    <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\n                      <mml:mi>p</mml:mi>\n                    </mml:math>\n                    -adic Hilbert spaces and applications","abstract":"<jats:p>\n                    We are concerned with some unbounded linear operators on the so-called\n                    <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\n                      <mml:mi>p</mml:mi>\n                    </mml:math>\n                    -adic Hilbert space\n                    <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\n                      <mml:msub>\n                        <mml:mi>𝔼</mml:mi>\n                        <mml:mi>ω</mml:mi>\n                      </mml:msub>\n                    </mml:math>\n                    . Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on\n                    <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\n                      <mml:msub>\n                        <mml:mi>𝔼</mml:mi>\n                        <mml:mi>ω</mml:mi>\n                      </mml:msub>\n                    </mml:math>\n                    , and the solvability of the equation\n                    <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\n                      <mml:mrow>\n                        <mml:mi>A</mml:mi>\n                        <mml:mi>u</mml:mi>\n                        <mml:mo>=</mml:mo>\n                        <mml:mi>v</mml:mi>\n                      </mml:mrow>\n                    </mml:math>\n                    where\n                    <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\n                      <mml:mi>A</mml:mi>\n                    </mml:math>\n                    is a linear operator on\n                    <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\n                      <mml:msub>\n                        <mml:mi>𝔼</mml:mi>\n                        <mml:mi>ω</mml:mi>\n                      </mml:msub>\n                    </mml:math>\n                    .\n                  </jats:p>","journal":"Annales mathématiques Blaise Pascal","year":2005,"id":36694,"datarank":0.48428781813629906,"base_score":2.1972245773362196,"endowment":2.1972245773362196,"self_citation_contribution":0.32958368660043297,"citation_network_contribution":0.15470413153586612,"self_endowment_contribution":0.32958368660043297,"citer_contribution":0.15470413153586612,"corpus_percentile":null,"corpus_rank":null,"citation_count":8,"citer_count":3,"citers_with_citation_signal":2,"citers_with_endowment":2,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":185374,"name":"Toka Diagana","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":2.1972245773362196,"endowment":2.1972245773362196,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"18998881","pmcid":null,"openalex_id":"https://openalex.org/W2332830220","authors":[],"funders":[],"total_grants":0,"fwci":1.2376,"citation_percentile":0.78243306,"influential_citations":1,"citation_trend":[{"year":2014,"count":1},{"year":2019,"count":2},{"year":2023,"count":1}],"oa_status":"gold","license":"cc-by","oa_locations":[{"url":"https://ambp.centre-mersenne.org/item/10.5802/ambp.203.pdf","host_type":"journal"},{"url":"https://doi.org/10.5802/ambp.203","host_type":"GOLD"},{"url":"https://ambp.centre-mersenne.org/item/10.5802/ambp.203.pdf","host_type":"publisher"},{"url":"https://ambp.centre-mersenne.org/articles/10.5802/ambp.203/","host_type":"repository"},{"url":"http://www.numdam.org/articles/10.5802/ambp.203/","host_type":"repository"}],"fields_of_study":["advanced mathematical theories","Algebraic and Geometric Analysis","Mathematics"],"mesh_terms":[],"keywords":["Hilbert space","Von Neumann's theorem","Mathematics","Unbounded operator","Linear operators","Linear map","Diagonal","Operator (biology)","Operator theory","Compact operator on Hilbert space","Pure mathematics","Hermitian adjoint","Mathematical analysis","Spectral theorem","Operator norm","Nuclear operator","Unitary operator","Algebra over a field","Multiplication operator","Quasinormal operator","Finite-rank operator","Compact operator","Banach space","Computer science","Geometry"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-10T17:05:47.481821Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}