@misc{10481/76680,
year = {2022},
month = {6},
url = {http://hdl.handle.net/10481/76680},
abstract = {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.},
organization = {Partially supported by MCIN/AEI/10.13039/501-100011033/FEDER, EU, project no. PGC2018-093332-B-I00},
organization = {Junta de Andalucía grants number A-FQM-242-UGR18 and FQM375},
organization = {Partially supported by NSF of China (12171251)},
organization = {Tianjin Natural Science Foundation (Grant No. 19JCY-BJC30200)},
organization = {IMAG–María de Maeztu grant CEX2020-001105-M/AEI/10.13039/501100011033},
organization = {Scientific Research, King Saud University},
organization = {Funding for open access charge: Universidad de Granada / CBUA},
publisher = {Elsevier},
keywords = {Rickart C⁎-algebra, JB⁎-algebra and JB⁎-triple Baer C⁎-algebra and JB⁎-algebra},
keywords = {Weakly order Rickart JB⁎-triple},
keywords = {Von Neumann regularity, Inner ideal},
title = {A projection–less approach to Rickart Jordan structures},
doi = {10.1016/j.jalgebra.2022.06.007},
author = {Garcés, Jorge J. and Li, Lei and Peralta Pereira, Antonio Miguel and Tahlawi, Haifa A.},
}