{"id":"https://openalex.org/W7225079595","doi":"https://doi.org/10.5281/zenodo.23732817","title":"When is the Gohberg\u2013Krupnik lower bound for aI+bH sharp?","display_name":"When is the Gohberg\u2013Krupnik lower bound for aI+bH sharp?","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225079595","doi":"https://doi.org/10.5281/zenodo.23732817"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23732817","doi":"https://doi.org/10.5281/zenodo.23732817","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23732817","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23732817","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114453126","display_name":"Dave Goel","orcid":"https://orcid.org/0009-0008-2494-1354","observed_orcids":["https://orcid.org/0009-0008-2494-1354"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Goel, Dave","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5114453126"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.6089000105857849,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.6089000105857849,"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":0.1923000067472458,"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":0.07079999893903732,"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/riesz-projection","display_name":"Riesz projection","score":0.8360000252723694},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"computer-assisted proof","score":0.6600000262260437},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"interval arithmetic","score":0.902999997138977},{"id":"https://openalex.org/keywords/lean-proof-assistant","display_name":"Lean proof assistant","score":0.7450000047683716},{"id":"https://openalex.org/keywords/non-self-adjoint-operators","display_name":"non-self-adjoint operators","score":0.5709999799728394}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.8216000199317932},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8165000081062317},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6823999881744385},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5486000180244446},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.515999972820282},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.49779999256134033},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.3637000024318695},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.36230000853538513},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.359499990940094},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27000001072883606},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26339998841285706},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23732817","doi":"https://doi.org/10.5281/zenodo.23732817","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23732817","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.23732818","doi":"https://doi.org/10.5281/zenodo.23732818","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23732818","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.23732817","doi":"https://doi.org/10.5281/zenodo.23732817","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23732817","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225090088","https://openalex.org/W4402951430","https://openalex.org/W1982245988","https://openalex.org/W7170188940","https://openalex.org/W1972753531","https://openalex.org/W7095689059","https://openalex.org/W2963769728","https://openalex.org/W7221199519","https://openalex.org/W4407133463","https://openalex.org/W7213369961"],"abstract_inverted_index":{"Let":[0],"P+":[1,318],"and":[2,21,25,47,54,64,67,88,104,112,153,164,206,221,238,264,287,310,319],"P\u2212":[3],"be":[4,192],"the":[5,9,19,22,92,98,124,182,188,201,217,229,245,248,275,278,302,307],"Riesz":[6],"projections":[7],"on":[8,181,199,239,292],"complex":[10],"space":[11],"Lp(T),":[12],"1":[13,159,224],"<":[14,16,160,162,225,227],"p":[15,85,136,161,207,226,266],"\u221e,":[17],"onto":[18],"nonnegative":[20],"negative":[23],"frequencies,":[24],"let":[26],"H":[27,258],"=":[28,37,43,49,169,212,267],"\u2212i(P+":[29],"\u2212":[30,45,139,214],"P\u2212),":[31],"so":[32],"that":[33,71,123,190],"aI":[34],"+":[35,39,51,62],"bH":[36],"\u03b1P+":[38],"\u03b2P\u2212":[40],"with":[41,187,306],"\u03b1":[42,89,203],"a":[44,50,57,240,261],"ib":[46],"\u03b2":[48,205],"ib.":[52],"Gohberg":[53],"Krupnik":[55],"gave":[56],"lower":[58],"bound":[59,93,125,230,279],"for":[60,128,148,233],"\u2016aI":[61],"bH\u2016p,":[63],"Hollenbeck,":[65],"Kalton":[66],"Verbitsky":[68],"(2003)":[69],"remarked":[70],"it":[72,81,105,144],"is":[73,82,94,101,106,110,115,126,145,231,250,280,285],"not":[74,95,102,146,273,281],"sharp":[75,96,107,127,147,232],"in":[76,253,301],"general.":[77],"We":[78,271],"characterize":[79],"when":[80,133],"sharp.":[83,282],"For":[84,158,223],"\u2260":[86,90],"2":[87,163,268],"0":[91],"whenever":[97,108],"ratio":[99,131,151,167],"\u03b2/\u03b1":[100,109,170],"real,":[103],"real":[111,130,150,166,184,219],"nonpositive.":[113],"There":[114],"an":[116,176,179,195],"explicitly":[117],"defined":[118],"p0":[119,134,228],"\u2248":[120],"1.2336026":[121],"such":[122],"every":[129],"exactly":[132],"\u2264":[135,137],"p0/(p0":[138],"1);":[140],"outside":[141],"this":[142],"interval":[143,290,308],"any":[149],"below":[152],"sufficiently":[154],"close":[155],"to":[156],"1.":[157],"each":[165],"\u03bb":[168,191,235],"\u2208":[171],"(0,":[172],"1)":[173],"we":[174],"give":[175],"exact":[177],"criterion:":[178],"inequality":[180],"positive":[183],"axis,":[185],"together":[186],"condition":[189],"smaller":[193],"than":[194],"explicit":[196],"threshold":[197],"depending":[198],"p;":[200],"symmetries":[202],"\u2194":[204,208],"p\u2032,":[209],"where":[210,277],"p\u2032":[211],"p/(p":[213],"1),":[215],"cover":[216],"remaining":[218],"ratios":[220,244],"exponents.":[222],"all":[234],"near":[236],"0,":[237],"band":[241],"of":[242,247,257,260,265,317],"intermediate":[243],"outcome":[246],"criterion":[249],"known":[251],"only":[252],"part.":[254],"The":[255,283,295],"cases":[256],"itself,":[259],"single":[262],"projection":[263],"are":[269],"classical.":[270],"do":[272],"determine":[274],"norm":[276,316],"proof":[284,304],"computer-assisted":[286],"uses":[288],"rigorous":[289],"arithmetic":[291],"compact":[293],"domains.":[294],"classification":[296],"has":[297],"also":[298],"been":[299],"proved":[300],"Lean":[303],"assistant,":[305],"computations":[309],"two":[311],"cited":[312],"theorems":[313],"(the":[314],"Hollenbeck\u2013Verbitsky":[315],"Cole's":[320],"theorem)":[321],"taken":[322],"as":[323],"given.":[324]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-11-03T00:00:00"}