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arXiv · 2202.08140

A projection--less approach to Rickart Jordan structures

Jorge J. Garcés·Lei Li·Antonio M. Peralta·Haifa M. Tahlawi
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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 $A$ 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 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.

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Jorge J. Garcés, Lei Li, Antonio M. Peralta, Haifa M. Tahlawi. 2022-02-16. A projection--less approach to Rickart Jordan structures. https://arxiv.org/abs/2202.08140

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