Singly generatedC *-algebras
We consider a $C*$-algebra $A$ generated by $k$ self-adjoint elements. We prove that, for $n \geqslant \sqrt {k - 1}$ , the algebra $M_n (A)$ is singly generated, i.e., generated by one non-self-adjoint element. We present an example of algebraA for which the property that $M_n (A)$ is singly gener...
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| Date: | 1999 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1999
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4707 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510867177603072 |
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| author | Rabanovych, V. I. Рабанович, В. И. Рабанович, В. И. |
| author_facet | Rabanovych, V. I. Рабанович, В. И. Рабанович, В. И. |
| author_sort | Rabanovych, V. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:11:43Z |
| description | We consider a $C*$-algebra $A$ generated by $k$ self-adjoint elements. We prove that, for $n \geqslant \sqrt {k - 1}$ , the algebra $M_n (A)$ is singly generated, i.e., generated by one non-self-adjoint element. We present an example of algebraA for which the property that $M_n (A)$ is singly generated implies the relation $n \geqslant \sqrt {k - 1}$. |
| first_indexed | 2026-03-24T03:03:49Z |
| format | Article |
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| id | umjimathkievua-article-4707 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:03:49Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/07/badad3f11269b2d75e98020934d88107.pdf |
| spelling | umjimathkievua-article-47072020-03-18T21:11:43Z Singly generatedC *-algebras Однопорожденные С*-алгебры Rabanovych, V. I. Рабанович, В. И. Рабанович, В. И. We consider a $C*$-algebra $A$ generated by $k$ self-adjoint elements. We prove that, for $n \geqslant \sqrt {k - 1}$ , the algebra $M_n (A)$ is singly generated, i.e., generated by one non-self-adjoint element. We present an example of algebraA for which the property that $M_n (A)$ is singly generated implies the relation $n \geqslant \sqrt {k - 1}$. Розглядається $С*$-алгебра $A$, породжена $k$ самоспряженими твірними. Доводиться, що при $n \geqslant \sqrt {k - 1}$ алгебра $M_n (A)$ є одиопородженою, тобто породжена одним несамоспряженим генератором. Наведено приклад алгебри А, для якої з одиопороджеиості $M_n (A)$ випливає, що $n \geqslant \sqrt {k - 1}$. Institute of Mathematics, NAS of Ukraine 1999-08-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4707 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 8 (1999); 1136-1141 Український математичний журнал; Том 51 № 8 (1999); 1136-1141 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4707/6116 https://umj.imath.kiev.ua/index.php/umj/article/view/4707/6117 Copyright (c) 1999 Rabanovych V. I. |
| spellingShingle | Rabanovych, V. I. Рабанович, В. И. Рабанович, В. И. Singly generatedC *-algebras |
| title | Singly generatedC *-algebras |
| title_alt | Однопорожденные С*-алгебры |
| title_full | Singly generatedC *-algebras |
| title_fullStr | Singly generatedC *-algebras |
| title_full_unstemmed | Singly generatedC *-algebras |
| title_short | Singly generatedC *-algebras |
| title_sort | singly generatedc *-algebras |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4707 |
| work_keys_str_mv | AT rabanovychvi singlygeneratedcalgebras AT rabanovičvi singlygeneratedcalgebras AT rabanovičvi singlygeneratedcalgebras AT rabanovychvi odnoporoždennyesalgebry AT rabanovičvi odnoporoždennyesalgebry AT rabanovičvi odnoporoždennyesalgebry |