On Amenability-Like Properties of a Class of Matrix Algebras
In this study, we show that a matrix algebra ℒℳIpA is a dual Banach algebra, where A is a dual Banach algebra and 1≤p≤2. We show that ℒℳIpℂ is Connes amenable if and only if I is finite, for every nonempty set I. Additionally, we prove that ℒℳIpℂ is always pseudo-Connes amenable, for 1≤p≤2. Also, Co...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/3194715 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832545948139520000 |
|---|---|
| author | M. Rostami S. F. Shariati A. Sahami |
| author_facet | M. Rostami S. F. Shariati A. Sahami |
| author_sort | M. Rostami |
| collection | DOAJ |
| description | In this study, we show that a matrix algebra ℒℳIpA is a dual Banach algebra, where A is a dual Banach algebra and 1≤p≤2. We show that ℒℳIpℂ is Connes amenable if and only if I is finite, for every nonempty set I. Additionally, we prove that ℒℳIpℂ is always pseudo-Connes amenable, for 1≤p≤2. Also, Connes amenability and approximate Connes biprojectivity are investigated for generalized upper triangular matrix algebras. Finally, we show that UpIpA∗∗ is approximately biflat if and only if A∗∗ is approximately biflat and I is a singleton. |
| format | Article |
| id | doaj-art-bf9341ec592042c28add28421c4b2676 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-bf9341ec592042c28add28421c4b26762025-02-03T07:24:17ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/3194715On Amenability-Like Properties of a Class of Matrix AlgebrasM. Rostami0S. F. Shariati1A. Sahami2Department of Mathematics and Computer ScienceDepartment of Mathematics and Computer ScienceDepartment of MathematicsIn this study, we show that a matrix algebra ℒℳIpA is a dual Banach algebra, where A is a dual Banach algebra and 1≤p≤2. We show that ℒℳIpℂ is Connes amenable if and only if I is finite, for every nonempty set I. Additionally, we prove that ℒℳIpℂ is always pseudo-Connes amenable, for 1≤p≤2. Also, Connes amenability and approximate Connes biprojectivity are investigated for generalized upper triangular matrix algebras. Finally, we show that UpIpA∗∗ is approximately biflat if and only if A∗∗ is approximately biflat and I is a singleton.http://dx.doi.org/10.1155/2022/3194715 |
| spellingShingle | M. Rostami S. F. Shariati A. Sahami On Amenability-Like Properties of a Class of Matrix Algebras Journal of Mathematics |
| title | On Amenability-Like Properties of a Class of Matrix Algebras |
| title_full | On Amenability-Like Properties of a Class of Matrix Algebras |
| title_fullStr | On Amenability-Like Properties of a Class of Matrix Algebras |
| title_full_unstemmed | On Amenability-Like Properties of a Class of Matrix Algebras |
| title_short | On Amenability-Like Properties of a Class of Matrix Algebras |
| title_sort | on amenability like properties of a class of matrix algebras |
| url | http://dx.doi.org/10.1155/2022/3194715 |
| work_keys_str_mv | AT mrostami onamenabilitylikepropertiesofaclassofmatrixalgebras AT sfshariati onamenabilitylikepropertiesofaclassofmatrixalgebras AT asahami onamenabilitylikepropertiesofaclassofmatrixalgebras |