2015/07/26 by Fatmah B. Jamjoom, Jamjoom, Fatmah B., Antonio M. Peralta +5
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1507.07186
openalex publication_date 2015/07/26 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
The aim of this note is to study Čebyšëv JB^*-subtriples of general JB^*-triples. It is established that if F is a non-zero Čebyšëv JB^*-subtriple of a JB^*-triple E, then exactly one of the following statements holds:\beginenumerate\item F is a rank one JBW^*-triple with dim(F)≥ 2 (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, \item F= ℂ e, where e is a complete tripotent in E, \item E and F are rank two JBW^*-triples, but F may have arbitrary dimension, \item F has rank greater or equal than three and E=F. \endenumerate