In this paper, $n$-quasitraces on real C*-algebras are studied. It is proved that if $R$ is a real C*-algebra, then the natural extension of an $n$-quasitrace of $R$ to $R+iR$ is also an $n$-quasitrace, and conversely, the restriction of an $n$-quasitrace from $R+iR$ to $R$ is also an $n$-quasitrace. In 1982, Blackadar and Handelman proved that every quasitrace on an AW*-algebra is a $2$-quasitrace. In this paper, a real analogue of that result is obtained. However, in the general case (i.e., for C*-algebras), this result does not hold. Using Kirchberg's example -- where a unital C*-algebra and its quasitrace are constructed such that the quasitrace is not a 2-quasitrace (and therefore is not a trace) -- a similar example is constructed in the real case. The paper also studies the properties of 2-quasitrace on real C*-algebras. As is known, Kaplansky asked whether every (2-) quasitrace on a C*-algebra linear, i.e., a trace. This question remains open to this day. Haagerup has a positive answer to this question in the case where the C*-algebra is unital and exact. In this paper, a real analogue of Haagerup's result is proved.
| Mualliflar | Ramazonova, L., Rakhimov, A. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2026-03-25 |
| Jild | 70 |
| Son | 1 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2026-1-20 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2026-1-20 · Maqolaning asl sahifasi
C*-algebras, AW*-algebras, quasitraces on C*- and AW*-algebras
| APA | Ramazonova, L., & Rakhimov, A. (2026). Quasitraces on exact real C*-algebras are traces. O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-20 |
|---|---|
| GOST (OAK) | Ramazonova, L., Rakhimov, A. Quasitraces on exact real C*-algebras are traces // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 1. – DOI: 10.29229/uzmj.2026-1-20. |
| MLA | Ramazonova, L., and Rakhimov, A. “Quasitraces on exact real C*-algebras are traces.” O‘zbekiston matematika jurnali, 70(1), 2026. https://doi.org/10.29229/uzmj.2026-1-20 |
| Chicago | Ramazonova, L., and Rakhimov, A. “Quasitraces on exact real C*-algebras are traces.” O‘zbekiston matematika jurnali, 70(1) (2026). https://doi.org/10.29229/uzmj.2026-1-20 |
| Harvard | Ramazonova, L., and Rakhimov, A (2026) ‘Quasitraces on exact real C*-algebras are traces’, O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-20 |
| BibTeX | @article{ramazonoval2026,
title = {Quasitraces on exact real C*-algebras are traces},
author = {Ramazonova, L. and Rakhimov, A.},
journal = {O‘zbekiston matematika jurnali},
year = {2026},
volume = {70},
number = {1},
doi = {10.29229/uzmj.2026-1-20},
url = {https://doi.org/10.29229/uzmj.2026-1-20}
} |
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