{"id":"https://openalex.org/W2168332816","doi":"https://doi.org/10.1155/2012/643568","title":"Norm for Sums of Two Basic Elementary Operators","display_name":"Norm for Sums of Two Basic Elementary Operators","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2168332816","doi":"https://doi.org/10.1155/2012/643568","mag":"2168332816"},"language":"en","primary_location":{"id":"doi:10.1155/2012/643568","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/643568","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/643568.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2012/643568.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013070274","display_name":"A\u200e. \u200eBachir","orcid":"https://orcid.org/0009-0003-3144-5942"},"institutions":[{"id":"https://openalex.org/I4210124230","display_name":"Universit\u00e9 Mustapha Stambouli de Mascara","ror":"https://ror.org/02vqddp65","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210124230"]},{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]},{"id":"https://openalex.org/I162489102","display_name":"University of Batna 1","ror":"https://ror.org/04hrbe508","country_code":"DZ","type":"education","lineage":["https://openalex.org/I162489102"]}],"countries":["DZ","SA"],"is_corresponding":true,"raw_author_name":"A. Bachir","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia","Department of Mathematics, Faculty of Science, University of Batna, 05000 Batna, Algeria","Department of Mathematics, Mascara University, Algeria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Batna, 05000 Batna, Algeria","institution_ids":["https://openalex.org/I162489102"]},{"raw_affiliation_string":"Department of Mathematics, Mascara University, Algeria","institution_ids":["https://openalex.org/I4210124230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007031361","display_name":"Farida Lombarkia","orcid":null},"institutions":[{"id":"https://openalex.org/I162489102","display_name":"University of Batna 1","ror":"https://ror.org/04hrbe508","country_code":"DZ","type":"education","lineage":["https://openalex.org/I162489102"]},{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]},{"id":"https://openalex.org/I4210124230","display_name":"Universit\u00e9 Mustapha Stambouli de Mascara","ror":"https://ror.org/02vqddp65","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210124230"]}],"countries":["DZ","SA"],"is_corresponding":false,"raw_author_name":"F. Lombarkia","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia","Department of Mathematics, Faculty of Science, University of Batna, 05000 Batna, Algeria","Department of Mathematics, Mascara University, Algeria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Batna, 05000 Batna, Algeria","institution_ids":["https://openalex.org/I162489102"]},{"raw_affiliation_string":"Department of Mathematics, Mascara University, Algeria","institution_ids":["https://openalex.org/I4210124230"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007020900","display_name":"Abdelkader Segres","orcid":null},"institutions":[{"id":"https://openalex.org/I162489102","display_name":"University of Batna 1","ror":"https://ror.org/04hrbe508","country_code":"DZ","type":"education","lineage":["https://openalex.org/I162489102"]},{"id":"https://openalex.org/I4210124230","display_name":"Universit\u00e9 Mustapha Stambouli de Mascara","ror":"https://ror.org/02vqddp65","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210124230"]},{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["DZ","SA"],"is_corresponding":false,"raw_author_name":"A. Segres","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia","Department of Mathematics, Faculty of Science, University of Batna, 05000 Batna, Algeria","Department of Mathematics, Mascara University, Algeria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Batna, 05000 Batna, Algeria","institution_ids":["https://openalex.org/I162489102"]},{"raw_affiliation_string":"Department of Mathematics, Mascara University, Algeria","institution_ids":["https://openalex.org/I4210124230"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013070274"],"corresponding_institution_ids":["https://openalex.org/I162489102","https://openalex.org/I4210124230","https://openalex.org/I82952536"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16910625,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2012","issue":null,"first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9998000264167786,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9994000196456909,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/mathematics","display_name":"Mathematics","score":0.9001808166503906},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6721265912055969},{"id":"https://openalex.org/keywords/numerical-range","display_name":"Numerical range","score":0.5739379525184631},{"id":"https://openalex.org/keywords/operator-norm","display_name":"Operator norm","score":0.5527116060256958},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4040437340736389},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36103469133377075},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.260001003742218}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9001808166503906},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6721265912055969},{"id":"https://openalex.org/C193060811","wikidata":"https://www.wikidata.org/wiki/Q1579053","display_name":"Numerical range","level":2,"score":0.5739379525184631},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.5527116060256958},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4040437340736389},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36103469133377075},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.260001003742218},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2012/643568","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/643568","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/643568.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:643568","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2012/643568.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:ed027d3f91b14a5baa68e5bd9b8d7fbd","is_oa":true,"landing_page_url":"https://doaj.org/article/ed027d3f91b14a5baa68e5bd9b8d7fbd","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/643568","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/643568","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/643568.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324433","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2168332816.pdf","grobid_xml":"https://content.openalex.org/works/W2168332816.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1486267208","https://openalex.org/W1492700492","https://openalex.org/W1531605312","https://openalex.org/W2009074818","https://openalex.org/W2046086057","https://openalex.org/W2070284561","https://openalex.org/W2077804224","https://openalex.org/W2119491605","https://openalex.org/W2168446344"],"related_works":["https://openalex.org/W3214582093","https://openalex.org/W2374649169","https://openalex.org/W2023111059","https://openalex.org/W2101854716","https://openalex.org/W3184166521","https://openalex.org/W2773403655","https://openalex.org/W2075149934","https://openalex.org/W4280563621","https://openalex.org/W2071887868","https://openalex.org/W4386164526"],"abstract_inverted_index":{"We":[0],"give":[1],"necessary":[2],"and":[3],"sufficient":[4],"conditions":[5],"under":[6],"which":[7],"the":[8,21],"norm":[9],"of":[10,20],"basic":[11],"elementary":[12],"operators":[13],"attains":[14],"its":[15],"optimal":[16],"value":[17],"in":[18],"terms":[19],"numerical":[22],"range.":[23]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}