@misc{10481/72097,
year = {2020},
month = {5},
url = {http://hdl.handle.net/10481/72097},
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.},
organization = {EPSRC (UK) project `Jordan Algebras, Finsler Geometry and Dynamics'	EP/R044228/1},
organization = {Spanish Ministry of Science, Innovation and Universities (MICINN)},
organization = {European Commission	PGC2018-093332-B-I00},
organization = {Junta de Andalucia	FQM375	
A-FQM-242-UGR18	
PY20_00255},
organization = {IMAG-Maria de Maeztu grant	CEX2020-001105-M/AEI/10.13039/501100011033	
MCIN/AEI/10.13039/501100011033/FEDER},
publisher = {Taylor & Francis},
keywords = {Isometry},
keywords = {Jordan ∗-isomorphism},
keywords = {Unitary set},
keywords = {JB∗-algebra},
keywords = {JBW*-algebra},
keywords = {Extension of isometries},
title = {Can one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries?},
doi = {10.1080/03081087.2021.2003745},
author = {Cueto Avellaneda, María and Peralta Pereira, Antonio Miguel},
}