{"id":"https://openalex.org/W7216456852","doi":"https://doi.org/10.48550/arxiv.2610.00816","title":"On the Shalit-Shamovich Spectral Radius","display_name":"On the Shalit-Shamovich Spectral Radius","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7216456852","doi":"https://doi.org/10.48550/arxiv.2610.00816"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.00816","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00816","pdf_url":"https://arxiv.org/pdf/2610.00816","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.00816","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119304644","display_name":"Maximilian Tornes","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tornes, Maximilian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5119304644"],"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9398999810218811,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9398999810218811,"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":0.049300000071525574,"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":0.006800000090152025,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/operator-tuples","display_name":"operator tuples","score":0.37599998712539673}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.757099986076355},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.7506999969482422},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.722599983215332},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.6561999917030334},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5965999960899353},{"id":"https://openalex.org/C176691602","wikidata":"https://www.wikidata.org/wiki/Q7097841","display_name":"Operator space","level":4,"score":0.5781000256538391},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.529699981212616},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5103999972343445},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.4887999892234802},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4853000044822693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4690999984741211},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.34209999442100525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34049999713897705},{"id":"https://openalex.org/C2778740170","wikidata":"https://www.wikidata.org/wiki/Q7575210","display_name":"Spectral space","level":2,"score":0.3305000066757202},{"id":"https://openalex.org/C186121230","wikidata":"https://www.wikidata.org/wiki/Q7575215","display_name":"Spectral theory of ordinary differential equations","level":5,"score":0.3172999918460846},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.28029999136924744},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C4839761","wikidata":"https://www.wikidata.org/wiki/Q212111","display_name":"Spectral line","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C2992500303","wikidata":"https://www.wikidata.org/wiki/Q5680845","display_name":"Operator matrix","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C24129628","wikidata":"https://www.wikidata.org/wiki/Q25345430","display_name":"Complex space","level":3,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.00816","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00816","pdf_url":"https://arxiv.org/pdf/2610.00816","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.2610.00816","doi":"https://doi.org/10.48550/arxiv.2610.00816","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.00816","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:2610.00816","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00816","pdf_url":"https://arxiv.org/pdf/2610.00816","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/W7216456852.pdf","grobid_xml":"https://content.openalex.org/works/W7216456852.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7160926417"],"related_works":["https://openalex.org/W7160926417","https://openalex.org/W2595506402","https://openalex.org/W7098267463","https://openalex.org/W4412637291","https://openalex.org/W2051394544","https://openalex.org/W1985462823","https://openalex.org/W4230412694","https://openalex.org/W2028793305","https://openalex.org/W7220650000","https://openalex.org/W1979567889"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,29],"the":[3,13,30,44,66,75],"spectral":[4,32,68],"radius":[5],"introduced":[6],"by":[7],"Shalit":[8,56],"and":[9,20,35,57,70],"Shamovich":[10],"uniquely":[11],"determines":[12],"underlying":[14],"operator":[15,23,87],"space":[16,24,88],"structure:":[17],"If":[18],"E_1":[19],"E_2":[21],"are":[22],"structures":[25],"on":[26,38,86],"C^d":[27],"such":[28],"corresponding":[31],"radii":[33],"\u03c1_{E_1}":[34],"\u03c1_{E_2}":[36],"agree":[37],"every":[39],"d-tuple":[40],"of":[41,54,82],"operators,":[42],"then":[43],"identity":[45],"map":[46],"is":[47],"completely":[48,76],"isometric.":[49],"This":[50],"answers":[51],"a":[52],"question":[53],"Scherer,":[55],"Shamovich.":[58],"Moreover,":[59],"we":[60],"obtain":[61],"an":[62,72],"analogous":[63],"result":[64],"for":[65,80],"minimal":[67],"radii,":[69],"showcase":[71],"application":[73],"to":[74],"bounded":[77,83],"isomorphism":[78],"problem":[79],"algebras":[81],"non-commutative":[84],"functions":[85],"unit":[89],"balls.":[90]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}
