A projection–less approach to Rickart Jordan structures
The main goal of this paper is to introduce and explore
an appropriate notion of weakly Rickart JB*-triples. We introduce weakly and weakly order Rickart JB*-triples, and we show that a C*-algebra A is a weakly (order) Rickart JB∗-triple precisely when it is a weakly Rickart C*-algebra. We also prove that the Peirce-2 subspace associated with any tripotent in a weakly order Rickart JB∗-triple is a Rickart JB*-algebra in the sense of Ayupov and Arzikulov. By extending a classical property of Rickart C-algebras, we prove that every weakly order Rickart JB*-triple is generated by its tripotents.
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…