{"id":"https://openalex.org/W2131980761","doi":"https://doi.org/10.1007/978-3-642-33469-6_4","title":"Invariant Subspaces for Operators with Thick Spectra","display_name":"Invariant Subspaces for Operators with Thick Spectra","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2131980761","doi":"https://doi.org/10.1007/978-3-642-33469-6_4","mag":"2131980761"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-33469-6_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-33469-6_4","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004805236","display_name":"Mingxue Liu","orcid":"https://orcid.org/0000-0002-6801-1705"},"institutions":[{"id":"https://openalex.org/I4210122543","display_name":"Guangdong Polytechnic Normal University","ror":"https://ror.org/02pcb5m77","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210122543"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Mingxue Liu","raw_affiliation_strings":["School of Computer Science and Technology, Guangdong Polytechnic Normal University, Guangzhou, 510665, People\u015b Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Guangdong Polytechnic Normal University, Guangzhou, 510665, People\u015b Republic of China","institution_ids":["https://openalex.org/I4210122543"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004805236"],"corresponding_institution_ids":["https://openalex.org/I4210122543"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25257732,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"22","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9984999895095825,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9977999925613403,"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/invariant-subspace-problem","display_name":"Invariant subspace problem","score":0.8941320180892944},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.8304870128631592},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.7587168216705322},{"id":"https://openalex.org/keywords/invariant-subspace","display_name":"Invariant subspace","score":0.727678656578064},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.67798912525177},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6577608585357666},{"id":"https://openalex.org/keywords/reflexive-operator-algebra","display_name":"Reflexive operator algebra","score":0.6079477667808533},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.5392789244651794},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5341381430625916},{"id":"https://openalex.org/keywords/von-neumann-architecture","display_name":"Von Neumann architecture","score":0.49874305725097656},{"id":"https://openalex.org/keywords/bounded-operator","display_name":"Bounded operator","score":0.439856618642807},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.41536960005760193},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3674609065055847},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3578398823738098},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3205406069755554},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30652177333831787},{"id":"https://openalex.org/keywords/approximation-property","display_name":"Approximation property","score":0.30577731132507324},{"id":"https://openalex.org/keywords/compact-operator","display_name":"Compact operator","score":0.20057451725006104},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15969929099082947},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15911197662353516},{"id":"https://openalex.org/keywords/unbounded-operator","display_name":"Unbounded operator","score":0.13683202862739563},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07896214723587036},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.0723961591720581}],"concepts":[{"id":"https://openalex.org/C109321718","wikidata":"https://www.wikidata.org/wiki/Q6059532","display_name":"Invariant subspace problem","level":5,"score":0.8941320180892944},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8304870128631592},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.7587168216705322},{"id":"https://openalex.org/C2777059694","wikidata":"https://www.wikidata.org/wiki/Q2706744","display_name":"Invariant subspace","level":3,"score":0.727678656578064},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.67798912525177},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6577608585357666},{"id":"https://openalex.org/C16324678","wikidata":"https://www.wikidata.org/wiki/Q7307359","display_name":"Reflexive operator algebra","level":4,"score":0.6079477667808533},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.5392789244651794},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5341381430625916},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.49874305725097656},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.439856618642807},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.41536960005760193},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3674609065055847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3578398823738098},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3205406069755554},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30652177333831787},{"id":"https://openalex.org/C152306953","wikidata":"https://www.wikidata.org/wiki/Q621744","display_name":"Approximation property","level":3,"score":0.30577731132507324},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.20057451725006104},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15969929099082947},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15911197662353516},{"id":"https://openalex.org/C2890095","wikidata":"https://www.wikidata.org/wiki/Q5108738","display_name":"Unbounded operator","level":4,"score":0.13683202862739563},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07896214723587036},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0723961591720581},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-33469-6_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-33469-6_4","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1489494202","https://openalex.org/W1526082579","https://openalex.org/W1540752844","https://openalex.org/W1626315639","https://openalex.org/W1964147941","https://openalex.org/W2013672160","https://openalex.org/W2021600464","https://openalex.org/W2030080723","https://openalex.org/W2063976990","https://openalex.org/W2076687762","https://openalex.org/W2095592327","https://openalex.org/W2327579976","https://openalex.org/W4254436387","https://openalex.org/W4255057637"],"related_works":["https://openalex.org/W2906892192","https://openalex.org/W3036384415","https://openalex.org/W2004626794","https://openalex.org/W4287755290","https://openalex.org/W3036347990","https://openalex.org/W4236206498","https://openalex.org/W2952523379","https://openalex.org/W4297580462","https://openalex.org/W2038755314","https://openalex.org/W3105005497"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
