Remarks on weak amenability of hypergroups
UDC 512.5 We study the existence of multiplier (completely) bounded approximate identities for the Fourier algebras of some classes of hypergroups. In particular, it is shown that, the hypergroups from a large class of commutative hypergroups are weakly amenable with the Cowling–Haagerup consta...
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| Дата: | 2026 |
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| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7943 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512816755113984 |
|---|---|
| author | Alaghmandan, Mahmood Alaghmandan, Mahmood |
| author_facet | Alaghmandan, Mahmood Alaghmandan, Mahmood |
| author_sort | Alaghmandan, Mahmood |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:38:24Z |
| description |
UDC 512.5
We study the existence of multiplier (completely) bounded approximate identities for the Fourier algebras of some classes of hypergroups. In particular, it is shown that, the hypergroups from a large class of commutative hypergroups are weakly amenable with the Cowling–Haagerup constant $1$. As a corollary, we answer an open question of Eymard about Jacobi hypergroups. We also characterize the existence of bounded approximate identities for the hypergroup Fourier algebras of spherical hypergroups.
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| doi_str_mv | 10.3842/umzh.v77i5.7943 |
| first_indexed | 2026-03-24T03:34:48Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7943 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:34:48Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-79432026-03-21T13:38:24Z Remarks on weak amenability of hypergroups Remarks on weak amenability of hypergroups Alaghmandan, Mahmood Alaghmandan, Mahmood weak amenability Fourier algebra completely bounded multipliers Leptin theorem ultraspherical hypergroups UDC 512.5 We study the existence of multiplier (completely) bounded approximate identities for the Fourier algebras of some classes of hypergroups. In particular, it is shown that, the hypergroups from a large class of commutative hypergroups are weakly amenable with the Cowling–Haagerup constant $1$. As a corollary, we answer an open question of Eymard about Jacobi hypergroups. We also characterize the existence of bounded approximate identities for the hypergroup Fourier algebras of spherical hypergroups. УДК 512.5 Зауваження щодо слабкої аменабельності гіпергруп Досліджено існування мультиплікативних (повністю) обмежених апроксимативних одиниць для алгебр Фур'є деяких класів гіпергруп. Зокрема, доведено, що широкий клас комутативних гіпергруп є слабко аменабельним із константою Ковлінга–Гаагерупа $1$. Як наслідок отримано відповідь на відкриту задачу Еймара, пов'язану з гіпергрупами Якобі. Крім того, встановлено умови існування обмежених апроксимативних одиниць для алгебр Фур'є сферичних гіпергруп. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7943 10.3842/umzh.v77i5.7943 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 5 (2025); 364–365 Український математичний журнал; Том 77 № 5 (2025); 364–365 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7943/10523 Copyright (c) 2025 Mahmood Alaghmandan |
| spellingShingle | Alaghmandan, Mahmood Alaghmandan, Mahmood Remarks on weak amenability of hypergroups |
| title | Remarks on weak amenability of hypergroups |
| title_alt | Remarks on weak amenability of hypergroups |
| title_full | Remarks on weak amenability of hypergroups |
| title_fullStr | Remarks on weak amenability of hypergroups |
| title_full_unstemmed | Remarks on weak amenability of hypergroups |
| title_short | Remarks on weak amenability of hypergroups |
| title_sort | remarks on weak amenability of hypergroups |
| topic_facet | weak amenability Fourier algebra completely bounded multipliers Leptin theorem ultraspherical hypergroups |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7943 |
| work_keys_str_mv | AT alaghmandanmahmood remarksonweakamenabilityofhypergroups AT alaghmandanmahmood remarksonweakamenabilityofhypergroups |