Abstract
The aim of this note is to study ebysev JB-subtriples of general JB-triples. It is established that if F is a non-zero ebysev JB-subtriple of a JB-triple E, then exactly one of the following statements holds:
(a) F is a rank one JBW-triple with dim (i.e. a complex Hilbert space regarded as a type 1 Cartan factor). Moreover, F may be a closed subspace of arbitrary dimension and E may have arbitrary rank;
(b) F = Ce, where e is a complete tripotent in E;
(c) E and F are rank two JBW*-triples, but F may have arbitrary dimension;
(d) F has rank greater or equal than three and E = F.