On generalized biderivations of Banach algebras
The aim of this paper is to introduce the concept of generalized biderivations of unital Banach algebras and prove some results concerning generalized biamenability of unital Banach algebras. Let $ A $ and $ B $ be unital Banach algebras, and let $ X $ be a unital $ A $-$ B $-module. Let $ T = Tri(A...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-12-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241720 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590769266884608 |
|---|---|
| author | Berna Arslan |
| author_facet | Berna Arslan |
| author_sort | Berna Arslan |
| collection | DOAJ |
| description | The aim of this paper is to introduce the concept of generalized biderivations of unital Banach algebras and prove some results concerning generalized biamenability of unital Banach algebras. Let $ A $ and $ B $ be unital Banach algebras, and let $ X $ be a unital $ A $-$ B $-module. Let $ T = Tri(A, X, B) $ be the corresponding triangular Banach algebra. We also study the generalized biamenability of triangular Banach algebras and show that if $ X = \{0\} $ and $ T $ is generalized biamenable, then $ A $ and $ B $ are both generalized biamenable. |
| format | Article |
| id | doaj-art-b27e998ba2e34a18adcff0ffc5ac1fca |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-b27e998ba2e34a18adcff0ffc5ac1fca2025-01-23T07:53:26ZengAIMS PressAIMS Mathematics2473-69882024-12-01912362593627210.3934/math.20241720On generalized biderivations of Banach algebrasBerna Arslan0Department of Mathematics, Aydın Adnan Menderes University, Aydın, TurkeyThe aim of this paper is to introduce the concept of generalized biderivations of unital Banach algebras and prove some results concerning generalized biamenability of unital Banach algebras. Let $ A $ and $ B $ be unital Banach algebras, and let $ X $ be a unital $ A $-$ B $-module. Let $ T = Tri(A, X, B) $ be the corresponding triangular Banach algebra. We also study the generalized biamenability of triangular Banach algebras and show that if $ X = \{0\} $ and $ T $ is generalized biamenable, then $ A $ and $ B $ are both generalized biamenable.https://www.aimspress.com/article/doi/10.3934/math.20241720generalized biderivationinner generalized biderivationgeneralized biamenabilityweak generalized biamenabilitytriangular banach algebra |
| spellingShingle | Berna Arslan On generalized biderivations of Banach algebras AIMS Mathematics generalized biderivation inner generalized biderivation generalized biamenability weak generalized biamenability triangular banach algebra |
| title | On generalized biderivations of Banach algebras |
| title_full | On generalized biderivations of Banach algebras |
| title_fullStr | On generalized biderivations of Banach algebras |
| title_full_unstemmed | On generalized biderivations of Banach algebras |
| title_short | On generalized biderivations of Banach algebras |
| title_sort | on generalized biderivations of banach algebras |
| topic | generalized biderivation inner generalized biderivation generalized biamenability weak generalized biamenability triangular banach algebra |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241720 |
| work_keys_str_mv | AT bernaarslan ongeneralizedbiderivationsofbanachalgebras |