A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A $C^*$ -ALGEBRA
It has been a long-standing question whether every amenable operator algebra is isomorphic to a (necessarily nuclear) $\mathrm{C}^*$ -algebra. In this note, we give a nonseparable counterexample. Finding...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2014-02-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509413000066/type/journal_article |
| _version_ | 1811156271752019968 |
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| author | YEMON CHOI ILIJAS FARAH NARUTAKA OZAWA |
| author_facet | YEMON CHOI ILIJAS FARAH NARUTAKA OZAWA |
| author_sort | YEMON CHOI |
| collection | DOAJ |
| description | It has been a long-standing question whether every amenable operator algebra is isomorphic to a (necessarily nuclear)
$\mathrm{C}^*$
-algebra. In this note, we give a nonseparable counterexample. Finding out whether a separable counterexample exists remains an open problem. We also initiate a general study of unitarizability of representations of amenable groups in
$\mathrm{C}^*$
-algebras and show that our method cannot produce a separable counterexample. |
| first_indexed | 2024-04-10T04:48:48Z |
| format | Article |
| id | doaj.art-e4550ce9ceab455bbf41b2046e2943cd |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:48:48Z |
| publishDate | 2014-02-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-e4550ce9ceab455bbf41b2046e2943cd2023-03-09T12:34:32ZengCambridge University PressForum of Mathematics, Sigma2050-50942014-02-01210.1017/fms.2013.6A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A $C^*$ -ALGEBRAYEMON CHOI0ILIJAS FARAH1NARUTAKA OZAWA2Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3 Matematicki Institut, Kneza Mihaila 35, Belgrade, SerbiaRIMS, Kyoto University, 606-8502 Japan;It has been a long-standing question whether every amenable operator algebra is isomorphic to a (necessarily nuclear) $\mathrm{C}^*$ -algebra. In this note, we give a nonseparable counterexample. Finding out whether a separable counterexample exists remains an open problem. We also initiate a general study of unitarizability of representations of amenable groups in $\mathrm{C}^*$ -algebras and show that our method cannot produce a separable counterexample.https://www.cambridge.org/core/product/identifier/S2050509413000066/type/journal_article47L30(primary); 46L0503E75 (secondary) |
| spellingShingle | YEMON CHOI ILIJAS FARAH NARUTAKA OZAWA A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A $C^*$ -ALGEBRA Forum of Mathematics, Sigma 47L30 (primary); 46L05 03E75 (secondary) |
| title | A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A $C^*$ -ALGEBRA |
| title_full | A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A $C^*$ -ALGEBRA |
| title_fullStr | A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A $C^*$ -ALGEBRA |
| title_full_unstemmed | A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A $C^*$ -ALGEBRA |
| title_short | A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A $C^*$ -ALGEBRA |
| title_sort | nonseparable amenable operator algebra which is not isomorphic to a c algebra |
| topic | 47L30 (primary); 46L05 03E75 (secondary) |
| url | https://www.cambridge.org/core/product/identifier/S2050509413000066/type/journal_article |
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