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- W4298266807 abstract "Let $T: Ato B$ be a (not necessarily surjective) linear isometry between two real JB$^*$-triples. Then for each $ain A$ there exists a tripotent $u_a$ in the bidual, $B'',$ of $B$ such that begin{enumerate}[$(a)$] item ${u_a,T({f,g,h}),u_a}={u_a,{T(f),T(g),T(h)},u_a}$, for all $f,g,h$ in the real JB$^*$-subtriple, $A_a,$ generated by $a$; item The mapping ${u_a,T(cdot),u_a} :A_arightarrow B''$ is a linear isometry. end{enumerate} Furthermore, when $B$ is a real C$^*$-algebra, the projection $p=p_a= u_a^* u_a$ satisfies that $T(cdot)p :A_arightarrow B''$ is an isometric triple homomorphism. When $A$ and $B$ are real C$^*$-algebras and $A$ is abelian of real type, then there exists a partial isometry $uin B''$ such that the mapping $T(cdot)u^*u :Arightarrow B''$ is an isometric triple homomorphism. These results generalise, to the real setting, some previous contributions due to C.-H. Chu and N.-C. Wong, and C.-H. Chu and M. Mackey in 2004 and 2005. We give an example of a non-surjective real linear isometry which cannot be complexified to a complex isometry, showing that the results in the real setting can not be derived by a mere complexification argument." @default.
- W4298266807 created "2022-10-01" @default.
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- W4298266807 date "2013-09-16" @default.
- W4298266807 modified "2023-09-29" @default.
- W4298266807 title "Linear isometries between real JB*-triples and C*-algebras" @default.
- W4298266807 doi "https://doi.org/10.48550/arxiv.1309.3838" @default.
- W4298266807 hasPublicationYear "2013" @default.
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