{"doi":"10.31197/atnaa.877757","title":"Spectral Theorem for Compact Self -Adjoint Operator in Γ -Hilbert space","abstract":"<jats:p xml:lang=\"en\">In this article we investigate some basic results of Self-adjoint Operator in Γ-Hilbert space. We proof some similar results on Self-adjoint Operator in this space with some specific norm. Finally we will prove that the Spectral Theorem for Compact Self-adjoint Operator in Γ -Hilbert space and the converse is true.</jats:p>","journal":"Advances in the Theory of Nonlinear Analysis and its Application","year":2022,"id":36686,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":0,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"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":185351,"name":"Sahın Injamamul ISLAM","orcid":"0000-0002-8587-7922","position":1,"is_corresponding":false},{"id":185352,"name":"Ashoke DAS","orcid":"0000-0002-6612-0182","position":2,"is_corresponding":false},{"id":185350,"name":"Nırmal SARKAR","orcid":"0000-0002-9050-1479","position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":0.0,"endowment":0.0,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"24523987","pmcid":null,"openalex_id":"https://openalex.org/W3217329814","authors":[],"funders":[],"total_grants":0,"fwci":0.0,"citation_percentile":0.28760901,"influential_citations":0,"citation_trend":[],"oa_status":"gold","license":null,"oa_locations":[{"url":"https://dergipark.org.tr/en/download/article-file/1567862","host_type":"journal"},{"url":"https://dergipark.org.tr/en/download/article-file/1567862","host_type":"GOLD"},{"url":"https://dergipark.org.tr/en/download/article-file/1567862","host_type":"publisher"},{"url":"https://doi.org/10.31197/atnaa.877757","host_type":"journal"},{"url":"https://dergipark.org.tr/tr/pub/atnaa/issue/64761/877757","host_type":""}],"fields_of_study":["Spectral Theory in Mathematical Physics","Numerical methods in inverse problems","Differential Equations and Boundary Problems","Mathematics"],"mesh_terms":[],"keywords":["Hilbert space","Mathematics","Compact operator on Hilbert space","Von Neumann's theorem","Hermitian adjoint","Weak operator topology","Self-adjoint operator","Quasinormal operator","Multiplication operator","Operator space","Compact operator","Nuclear operator","Operator (biology)","Rigged Hilbert space","Hilbert manifold","Converse","Operator norm","Norm (philosophy)","Unitary operator","Pure mathematics","Finite-rank operator","Extension (predicate logic)","Computer science","Banach space"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-10T17:05:08.891758Z","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":[]}