@misc{10481/69509,
year = {2021},
month = {4},
url = {http://hdl.handle.net/10481/69509},
abstract = {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.},
organization = {Spanish Ministry of Science, Innovation and Universities (MICINN)},
organization = {European Commission

PGC2018-093332-B-I00},
organization = {Programa Operativo FEDER 2014-2020},
organization = {Junta de Andalucia

A-FQM-242-UGR18},
organization = {Junta de Andalucia

FQM375},
publisher = {Elsevier},
keywords = {(Real-linear) isometry},
keywords = {Jordan ∗-isomorphism},
keywords = {Invertible elements},
keywords = {Jordan-Banach algebra},
keywords = {JB∗-algebra},
keywords = {Extension of isometries},
title = {Surjective isometries between sets of invertible elements in unital Jordan-Banach algebras},
doi = {10.1016/j.jmaa.2021.125284},
author = {Peralta Pereira, Antonio Miguel},
}