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A projection–less approach to Rickart Jordan structures

dc.contributor.authorGarcés, Jorge J.
dc.contributor.authorLi, Lei
dc.contributor.authorPeralta Pereira, Antonio Miguel 
dc.contributor.authorTahlawi, Haifa A.
dc.date.accessioned2022-09-13T11:15:35Z
dc.date.available2022-09-13T11:15:35Z
dc.date.issued2022-06-22
dc.identifier.citationJ.J. Garcés et al. A projection–less approach to Rickart Jordan structures. Journal of Algebra 609 (2022) 567–605 [https://doi.org/10.1016/j.jalgebra.2022.06.007]es_ES
dc.identifier.urihttp://hdl.handle.net/10481/76680
dc.descriptionAcknowledgments We would like to express our gratitude to the anonymous referee for many constructive comments and suggestions to improve the final form of the paper. J. Garcés and A.M. Peralta partially supported by MCIN/AEI/10.13039/501-100011033/FEDER, EU, project no. PGC2018-093332-B-I00 and Junta de Andalucía grants number A-FQM-242-UGR18 and FQM375. L. Li partially supported by NSF of China (12171251) and Tianjin Natural Science Foundation (Grant No. 19JCY-BJC30200). A.M. Peralta is also supported by the IMAG–María de Maeztu grant CEX2020-001105-M/AEI/10.13039/501100011033. H. Tahlawi supported by a grant of Scientific Research, King Saud University. Funding for open access charge: Universidad de Granada / CBUA.es_ES
dc.description.abstractThe 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.es_ES
dc.description.sponsorshipPartially supported by MCIN/AEI/10.13039/501-100011033/FEDER, EU, project no. PGC2018-093332-B-I00es_ES
dc.description.sponsorshipJunta de Andalucía grants number A-FQM-242-UGR18 and FQM375es_ES
dc.description.sponsorshipPartially supported by NSF of China (12171251)es_ES
dc.description.sponsorshipTianjin Natural Science Foundation (Grant No. 19JCY-BJC30200)es_ES
dc.description.sponsorshipIMAG–María de Maeztu grant CEX2020-001105-M/AEI/10.13039/501100011033es_ES
dc.description.sponsorshipScientific Research, King Saud Universityes_ES
dc.description.sponsorshipFunding for open access charge: Universidad de Granada / CBUAes_ES
dc.language.isoenges_ES
dc.publisherElsevieres_ES
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectRickart C⁎-algebra, JB⁎-algebra and JB⁎-triple Baer C⁎-algebra and JB⁎-algebraes_ES
dc.subjectWeakly order Rickart JB⁎-triplees_ES
dc.subjectVon Neumann regularity, Inner ideales_ES
dc.titleA projection–less approach to Rickart Jordan structureses_ES
dc.typejournal articlees_ES
dc.rights.accessRightsopen accesses_ES
dc.identifier.doi10.1016/j.jalgebra.2022.06.007
dc.type.hasVersionVoRes_ES


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