{"id":"https://openalex.org/W7206187693","doi":"https://doi.org/10.48550/arxiv.2609.00037","title":"On the $\u03c1$-numerical radius of rank-one operators and parametrized Buzano-type inequalities","display_name":"On the $\u03c1$-numerical radius of rank-one operators and parametrized Buzano-type inequalities","publication_year":2026,"publication_date":"2026-08-29","ids":{"openalex":"https://openalex.org/W7206187693","doi":"https://doi.org/10.48550/arxiv.2609.00037"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.00037","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.00037","pdf_url":"https://arxiv.org/pdf/2609.00037","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.00037","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014521495","display_name":"Hranislav Stankovi\u0107","orcid":"https://orcid.org/0000-0002-3418-9177","observed_orcids":["https://orcid.org/0000-0002-3418-9177"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Stankovi\u0107, Hranislav","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5014521495"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"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/T11545","display_name":"Advanced Banach Space Theory","score":9.999999747378752e-05,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rank-one-operators","display_name":"rank one operators","score":0.9890000224113464},{"id":"https://openalex.org/keywords/numerical-radius","display_name":"numerical radius","score":0.6800000071525574},{"id":"https://openalex.org/keywords/operator-norm","display_name":"operator norm","score":0.7720000147819519},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"spectral radius","score":0.996999979019165},{"id":"https://openalex.org/keywords/vector-inequalities","display_name":"vector inequalities","score":0.6029999852180481},{"id":"https://openalex.org/keywords/cauchy-schwarz-inequality","display_name":"Cauchy-Schwarz inequality","score":0.8259999752044678},{"id":"https://openalex.org/keywords/hilbert-space-operators","display_name":"Hilbert space operators","score":0.7429999709129333}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8163999915122986},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7419999837875366},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5616999864578247},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5340999960899353},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5033000111579895},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4560000002384186},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.41280001401901245},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.3977999985218048},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.3882000148296356},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.384799987077713},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3540000021457672},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.3483000099658966},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3375000059604645},{"id":"https://openalex.org/C2992500303","wikidata":"https://www.wikidata.org/wiki/Q5680845","display_name":"Operator matrix","level":2,"score":0.3353999853134155},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.32839998602867126},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3199000060558319},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2581000030040741},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.25369998812675476},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2529999911785126},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25110000371932983},{"id":"https://openalex.org/C60064506","wikidata":"https://www.wikidata.org/wiki/Q1262627","display_name":"Rigged Hilbert space","level":4,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.00037","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.00037","pdf_url":"https://arxiv.org/pdf/2609.00037","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2609.00037","doi":"https://doi.org/10.48550/arxiv.2609.00037","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.00037","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.00037","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.00037","pdf_url":"https://arxiv.org/pdf/2609.00037","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7206187693.pdf","grobid_xml":"https://content.openalex.org/works/W7206187693.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W6948339987","https://openalex.org/W7213224525","https://openalex.org/W7203701876","https://openalex.org/W4409191845","https://openalex.org/W7130520634","https://openalex.org/W4402699031","https://openalex.org/W7119112981","https://openalex.org/W4317490006","https://openalex.org/W7214343434","https://openalex.org/W164846852"],"abstract_inverted_index":{"Let":[0],"$\\mathcal{H}$":[1],"be":[2,103],"a":[3,28,55,74,122],"complex":[4],"Hilbert":[5,83],"space":[6],"and":[7,39,47,110,114],"$\u03c1>0$.":[8],"We":[9,64],"establish":[10],"the":[11,22,33,36,40,87,91,99,108,111,115],"explicit":[12,69],"formula":[13],"\\[":[14],"\u03c9_\u03c1(a\\otimes":[15],"b)=\\frac{1}\u03c1\\|a\\|":[16],"\\|b\\|+\\left|1-\\frac{1}\u03c1\\right||\\langle":[17],"a,b\\rangle|,\\qquad":[18],"a,b\\in\\mathcal{H},":[19],"\\]":[20],"for":[21,61],"$\u03c1$-numerical":[23],"radius":[24],"of":[25,58,130],"rank-one":[26],"operators,":[27],"unified":[29],"expression":[30],"interpolating":[31],"between":[32],"operator":[34],"norm,":[35],"numerical":[37],"radius,":[38,42],"spectral":[41],"which":[43,77,125],"correspond":[44],"to":[45],"$\u03c1=1,2$,":[46],"$\u03c1\\to\\infty$,":[48],"respectively.":[49],"As":[50],"an":[51,68,127],"application,":[52],"we":[53,85],"derive":[54],"parametrized":[56],"family":[57,92],"Buzano-type":[59],"inequalities":[60],"four":[62],"vectors.":[63],"extract":[65],"from":[66],"it":[67],"closed-form":[70],"bound":[71,89],"and,":[72],"under":[73],"reality":[75],"condition":[76],"is":[78,119],"automatically":[79],"satisfied":[80],"in":[81,90,93],"real":[82],"spaces,":[84],"determine":[86],"best":[88],"closed":[94],"form.":[95],"Examples":[96],"show":[97],"that":[98],"resulting":[100],"bounds":[101],"can":[102],"strictly":[104],"sharper":[105],"than":[106],"both":[107],"Cauchy--Schwarz":[109],"Buzano":[112,117],"inequality,":[113],"classical":[116],"inequality":[118],"recovered":[120],"as":[121],"boundary":[123],"case,":[124],"yields":[126],"alternative":[128],"proof":[129],"it.":[131]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-03T00:00:00"}