$M$-ideals, yet again: the case of real JB${}^{\ast }$-triples

David P. Blecher, Matthew Neal, Antonio M. Peralta +1

We prove that a subspace of a real JBW${}^{\ast }$-triple is an $M$-summand if and only if it is a weak${}^{\ast }$-closed triple ideal. As a consequence, $M$-ideals of real JB${}^{\ast }$-triples corresp…