{"doi":"10.1090/s0002-9939-1993-1155595-6","title":"Subspaces and graphs","abstract":"<p>\n                    Subspaces sufficiently near an arbitrary (fixed) subspace of a Hilbert space are shown to be in one-to-one correspondence with operators defined on the given subspace. Specifically, the nearby subspaces can be regarded as the graphs of these operators. This is applied to explicitly define a\n                    <inline-formula content-type=\"math/mathml\">\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript normal infinity\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:msup>\n                              <mml:mi>C</mml:mi>\n                              <mml:mi mathvariant=\"normal\">\n                                ∞\n                                \n                              </mml:mi>\n                            </mml:msup>\n                          </mml:mrow>\n                          <mml:annotation encoding=\"application/x-tex\">{C^\\infty }</mml:annotation>\n                        </mml:semantics>\n                      </mml:math>\n                    </inline-formula>\n                    -atlas of charts for the set of subspaces.\n                  </p>","journal":"Proceedings of the American Mathematical Society","year":1993,"id":14408,"datarank":0.547670382193568,"base_score":1.9459101490553132,"endowment":1.9459101490553132,"self_citation_contribution":0.29188652235829704,"citation_network_contribution":0.2557838598352709,"self_endowment_contribution":0.29188652235829704,"citer_contribution":0.2557838598352709,"corpus_percentile":null,"corpus_rank":null,"citation_count":6,"citer_count":5,"citers_with_citation_signal":4,"citers_with_endowment":4,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":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":113925,"name":"Kin Yan Chung","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":1.9459101490553132,"endowment":1.9459101490553132,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"24259432","pmcid":null,"openalex_id":"https://openalex.org/W2008470094","authors":[],"funders":[],"total_grants":0,"fwci":0.6396,"citation_percentile":0.75060016,"influential_citations":0,"citation_trend":[{"year":2014,"count":1},{"year":2025,"count":1}],"oa_status":"bronze","license":null,"oa_locations":[{"url":"https://www.ams.org/proc/1993-119-01/S0002-9939-1993-1155595-6/S0002-9939-1993-1155595-6.pdf","host_type":"journal"},{"url":"https://www.ams.org/proc/1993-119-01/S0002-9939-1993-1155595-6/S0002-9939-1993-1155595-6.pdf","host_type":"BRONZE"},{"url":"https://www.ams.org/proc/1993-119-01/S0002-9939-1993-1155595-6/S0002-9939-1993-1155595-6.pdf","host_type":"publisher"},{"url":"http://www.ams.org/proc/1993-119-01/S0002-9939-1993-1155595-6/S0002-9939-1993-1155595-6.pdf","host_type":"publisher"},{"url":"https://doi.org/10.1090/s0002-9939-1993-1155595-6","host_type":"journal"}],"fields_of_study":["Probabilistic and Robust Engineering Design","Lanthanide and Transition Metal Complexes","Spectral Theory in Mathematical Physics","Mathematics"],"mesh_terms":[],"keywords":["Linear subspace","Subspace topology","Hilbert space","Computer science","Annotation","Algorithm","Mathematics","Artificial intelligence","Pure mathematics"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-01T09:34:04.021744Z","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":[]}