Inner ideals, compact tripotents and Čebyšëv subtriples of JB<span class="a-plus-plus inline-equation id-i-eq1"> <span class="a-plus-plus equation-source format-t-e-x" xmlns:search="http://marklogic.com/appservices/search">\(^{*}\)span> span>-triples and C<span class="a-plus-plus inline-equation id-i-eq2"> <span class="a-plus-plus equation-sou
文摘
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:(a)F is a rank one JBW\(^*\)-triple with dim \((F)\ge 2\) (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;