Uniqueness of Hahn--Banach extensions and inner ideals in real C${}^{\ast }$-algebras and real JB${}^{\ast }$-triples

Lei Li, Antonio M. Peralta, Shanshan Su +1

We show that every closed (resp., weak${}^{\ast }$-closed) inner ideal $I$ of a real JB${}^{\ast }$-triple (resp. a real JBW${}^{\ast }$-triple) $E$ is Hahn--Banach smooth (resp., weak${}^{\ast }$-Hahn--Banach sm…