{"paper":{"title":"Linear isometries between real JB*-triples and C*-algebras","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, Maria Apazoglou","submitted_at":"2013-09-16T07:27:52Z","abstract_excerpt":"Let $T: A\\to B$ be a (not necessarily surjective) linear isometry between two real JB$^*$-triples. Then for each $a\\in A$ 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 $\\{u_a,T(\\cdot),u_a\\} :A_a\\rightarrow B''$ 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 $T(\\cdot)p :A_a\\rightarrow B''$ is an isometric trip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3838","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}