Inner ideals, compact tripotents and Cebyšëv subtriples of JB*-triples and C*-algebras
The aim of this note is to study Cebyšëv JB*-subtriples of general JB*-triples. It is established that if F is a non-zero Cebyšëv 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) ≥ 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;
(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.
We establish new estimates to compute the λ-function of Aron and Lohman on the unit ball of a
JB*-triple. It is established that for every Brown–Pedersen quasi-invertible element a in a JB*-…
We introduce and study the class of extremally rich JB∗-triples. We establish new results to determine the distance from an element a in an extremally rich JB∗-triple E to the set ∂e(E1) of all…
The aim of this note is to study Cebyšëv JB*-subtriples of general JB*-triples. It is established that if F is a non-zero Cebyšëv JB*-subtriple of a JB*-triple E, then exactly one of the following…