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Can one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries?
dc.contributor.author | Cueto Avellaneda, María | |
dc.contributor.author | Peralta Pereira, Antonio Miguel | |
dc.date.accessioned | 2021-12-16T13:24:38Z | |
dc.date.available | 2021-12-16T13:24:38Z | |
dc.date.issued | 2020-05-10 | |
dc.identifier.citation | Published 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.uri | http://hdl.handle.net/10481/72097 | |
dc.description | First 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.abstract | Let 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.sponsorship | EPSRC (UK) project `Jordan Algebras, Finsler Geometry and Dynamics' EP/R044228/1 | es_ES |
dc.description.sponsorship | Spanish Ministry of Science, Innovation and Universities (MICINN) | es_ES |
dc.description.sponsorship | European Commission PGC2018-093332-B-I00 | es_ES |
dc.description.sponsorship | Junta de Andalucia FQM375 A-FQM-242-UGR18 PY20_00255 | es_ES |
dc.description.sponsorship | IMAG-Maria de Maeztu grant CEX2020-001105-M/AEI/10.13039/501100011033 MCIN/AEI/10.13039/501100011033/FEDER | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | Taylor & Francis | es_ES |
dc.rights | Atribución-NoComercial-SinDerivadas 3.0 España | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.subject | Isometry | es_ES |
dc.subject | Jordan ∗-isomorphism | es_ES |
dc.subject | Unitary set | es_ES |
dc.subject | JB∗-algebra | es_ES |
dc.subject | JBW*-algebra | es_ES |
dc.subject | Extension of isometries | es_ES |
dc.title | Can one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries? | es_ES |
dc.type | journal article | es_ES |
dc.rights.accessRights | open access | es_ES |
dc.identifier.doi | 10.1080/03081087.2021.2003745 | |
dc.type.hasVersion | SMUR | es_ES |