The paper studies quasitraces on real C*-algebras, and AW*-completion of C*-subalgebras with respect to the $d_\tau$-metric generated by quasitrace $\tau$. It is proved that the $d_\tau$-closure of unital real C*-subalgebra $B$ of real C*-algebra $R$ is the smallest real AW*-subalgebra of $R$ containing $B$. To prove this, it was necessary to obtain a key result concerning the maximal Abelian self-adjoint subalgebra (masa), in connection with which Abelian algebras are studied separately. It is proved that for a compact Hausdorff space $X$ the algebra $C_r(X)$ of all continuous real functions on $X$ is a real abelian AW*-algebra if and only if $X$ is Stonean. Moreover, it has been proven that a unital real C*-algebra is a real AW*-algebra if and only if every masa has Stonean spectrum, and this is equivalent to the fact that every masa is monotone complete.
| Mualliflar | Rakhmonova, N. |
|---|---|
| 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.2026-1-19 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2026-1-19 · Maqolaning asl sahifasi
{Real C*-algebras, AW*-algebras, quasitrace, monotone completeness, maximal abelian self-adjoint subalgebra (masa).}
| APA | Rakhmonova, N. (2026). Normality of quasitrace and AW*-completion of the real C*-subalgebras. O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-19 |
|---|---|
| GOST (OAK) | Rakhmonova, N. Normality of quasitrace and AW*-completion of the real C*-subalgebras // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 1. – DOI: 10.29229/uzmj.2026-1-19. |
| MLA | Rakhmonova, N. “Normality of quasitrace and AW*-completion of the real C*-subalgebras.” O‘zbekiston matematika jurnali, 70(1), 2026. https://doi.org/10.29229/uzmj.2026-1-19 |
| Chicago | Rakhmonova, N. “Normality of quasitrace and AW*-completion of the real C*-subalgebras.” O‘zbekiston matematika jurnali, 70(1) (2026). https://doi.org/10.29229/uzmj.2026-1-19 |
| Harvard | Rakhmonova, N (2026) ‘Normality of quasitrace and AW*-completion of the real C*-subalgebras’, O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-19 |
| BibTeX | @article{rakhmonovan2026,
title = {Normality of quasitrace and AW*-completion of the real C*-subalgebras},
author = {Rakhmonova, N.},
journal = {O‘zbekiston matematika jurnali},
year = {2026},
volume = {70},
number = {1},
doi = {10.29229/uzmj.2026-1-19},
url = {https://doi.org/10.29229/uzmj.2026-1-19}
} |
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