A projection--less approach to Rickart Jordan structures
Operator Algebras
2022-02-17 v1
Abstract
The main goal of this paper is to introduce and explore an appropriate notion of weakly Rickart JB-triples. We introduce weakly order Rickart JB-triples, and we show that a C-algebra 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 a 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.
Keywords
Cite
@article{arxiv.2202.08140,
title = {A projection--less approach to Rickart Jordan structures},
author = {Jorge J. Garcés and Lei Li and Antonio M. Peralta and Haifa M. Tahlawi},
journal= {arXiv preprint arXiv:2202.08140},
year = {2022}
}