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dc.contributor.authorCueto Avellaneda, María
dc.contributor.authorPeralta Pereira, Antonio Miguel 
dc.date.accessioned2021-12-16T13:24:38Z
dc.date.available2021-12-16T13:24:38Z
dc.date.issued2020-05-10
dc.identifier.citationPublished version: María Cueto-Avellaneda & Antonio M. Peralta (2021) Can one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries?, Linear and Multilinear Algebra, DOI: [10.1080/03081087.2021.2003745]es_ES
dc.identifier.urihttp://hdl.handle.net/10481/72097
dc.descriptionFirst author supported by EPSRC (UK) project `Jordan Algebras, Finsler Geometry and Dynamics' ref. no. EP/R044228/1 and by the Spanish Ministry of Science, Innovation and Universities (MICINN) and European Regional Development Fund project no. PGC2018-093332-B-I00, and Consejeria de Economia, Innovacion, Ciencia y Empleo, Junta de Andalucia grants FQM375 and A-FQM-242-UGR18. Second author supported by MCIN/AEI/10.13039/501100011033/FEDER `Una manera de hacer Europa' project no. PGC2018-093332-B-I00, Consejeria de Economia, Innovacion, Ciencia y Empleo, Junta de Andalucia grants FQM375, A-FQM-242-UGR18 and PY20_00255, and by the IMAG-Maria de Maeztu grant CEX2020-001105-M/AEI/10.13039/501100011033.es_ES
dc.description.abstractLet M and N be two unital JB*-algebras and let U(M) and U(N) denote the sets of all unitaries in M and N, respectively. We prove that the following statements are equivalent: (a) M and N are isometrically isomorphic as (complex) Banach spaces; (b) M and N are isometrically isomorphic as real Banach spaces; (c) there exists a surjective isometry Delta : U(M) -> U(N). We actually establish a more general statement asserting that, under some mild extra conditions, for each surjective isometry Delta : U(M) -> U(N), we can find a surjective real linear isometry Psi : M -> N which coincides with Delta on the subset e(iMsa). If we assume that M and N are JBW*-algebras, then every surjective isometry Delta : U(M) -> U(N) admits a (unique) extension to a surjective real linear isometry from M onto N. This is an extension of the Hatori-Molnar theorem to the setting of JB*-algebras.es_ES
dc.description.sponsorshipEPSRC (UK) project `Jordan Algebras, Finsler Geometry and Dynamics' EP/R044228/1es_ES
dc.description.sponsorshipSpanish Ministry of Science, Innovation and Universities (MICINN)es_ES
dc.description.sponsorshipEuropean Commission PGC2018-093332-B-I00es_ES
dc.description.sponsorshipJunta de Andalucia FQM375 A-FQM-242-UGR18 PY20_00255es_ES
dc.description.sponsorshipIMAG-Maria de Maeztu grant CEX2020-001105-M/AEI/10.13039/501100011033 MCIN/AEI/10.13039/501100011033/FEDERes_ES
dc.language.isoenges_ES
dc.publisherTaylor & Francises_ES
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subjectIsometryes_ES
dc.subjectJordan ∗-isomorphismes_ES
dc.subjectUnitary setes_ES
dc.subjectJB∗-algebraes_ES
dc.subjectJBW*-algebraes_ES
dc.subjectExtension of isometrieses_ES
dc.titleCan one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries?es_ES
dc.typejournal articlees_ES
dc.rights.accessRightsopen accesses_ES
dc.identifier.doi10.1080/03081087.2021.2003745
dc.type.hasVersionSMURes_ES


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