Surjective isometries between sets of invertible elements in unital Jordan-Banach algebras Peralta Pereira, Antonio Miguel (Real-linear) isometry Jordan ∗-isomorphism Invertible elements Jordan-Banach algebra JB∗-algebra Extension of isometries Author partially supported by the Spanish Ministry of Science, Innovation and Universities (MICINN) and European Regional Development Fund project no. PGC2018093332BI00, Programa Operativo FEDER 2014-2020 and Consejeria de Economia y Conocimiento de la Junta de Andalucia grant number AFQM242UGR18, and Junta de Andalucia grant FQM375. The author would like to express his gratitude to the anonymous referees who generously spent their precious time in the review process of this paper. Referees' contributions are fundamental in the world of academia, in this case their valuable comments and suggestions allowed us to elude certain difficulties in some of the original arguments, and improved the final form of the manuscript. Let Mand Nbe complex unital Jordan-Banach algebras, and let M−1and N−1denote the sets of invertible elements in Mand N, respectively. Suppose that M ⊆M−1and N ⊆N−1are clopen subsets of M−1and N−1, respectively, which are closed for powers, inverses and products of the form Ua(b). In this paper we prove that for each surjective isometry Δ :M →Nthere exists a surjective real-linear isometry T0:M→Nand an element u0in the McCrimmon radical of Nsuch that Δ(a) =T0(a) +u0for all a ∈M. Assuming that Mand Nare unital JB∗-algebras we establish that for each surjective isometry Δ :M →Nthe element Δ(1) =uis a unitary element in Nand there exist a central projection p ∈Mand a complex-linear Jordan ∗-isomorphism Jfrom Monto the u∗-homotope Nu∗such that Δ(a) = J(p ◦ a) + J((1 − p) ◦ a ∗), for all a ∈M. Under the additional hypothesis that there is a unitary element ω0in Nsatisfying Uω0(Δ(1)) =1, we show the existence of a central projection p ∈Mand a complex-linear Jordan ∗-isomorphism Φfrom Monto Nsuch that Δ(a) = Uw∗ 0 (Φ(p ◦ a) + Φ((1 − p) ◦ a ∗)) , for all a ∈M. 2021-07-05T09:53:26Z 2021-07-05T09:53:26Z 2021-04-29 info:eu-repo/semantics/article Antonio M. Peralta, Surjective isometries between sets of invertible elements in unital Jordan-Banach algebras, Journal of Mathematical Analysis and Applications, Volume 502, Issue 2, 2021, 125284, ISSN 0022-247X, [https://doi.org/10.1016/j.jmaa.2021.125284] http://hdl.handle.net/10481/69509 10.1016/j.jmaa.2021.125284 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España Elsevier