Volume 9, Issue 4 (12-2023)                   mmr 2023, 9(4): 178-185 | Back to browse issues page

XML Persian Abstract Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Maysami Sadr M. A Result on the diagonal of contractible operator Banach algebras. mmr 2023; 9 (4) :178-185
URL: http://mmr.khu.ac.ir/article-1-3291-en.html
Department of Mathematics , sadr@iasbs.ac.ir
Abstract:   (433 Views)
A Banach algebra A is called contractible if for any Banach A-bimodule E, every continuous derivation from A into E is inner. One of the oldest unconfirmed conjectures in amenability  says that every contractible Banach algebra is finite dimensional. It is well-known that a Banach algebra A is contractible if and only if its unital and has a diagonal, that is a member M in the Banach algebra AπA such that satisfies in (M)=1 and a⊗1M=M(1⊗a) for every a in A. In this note we show that any diagonal of a contractible Banach algebra of operators on an infinite dimensional Banach space has a specific null property.
 
Full-Text [PDF 246 kb]   (172 Downloads)    
Type of Study: S | Subject: Anal
Received: 2022/10/8 | Revised: 2024/04/7 | Accepted: 2023/05/30 | Published: 2024/02/17 | ePublished: 2024/02/17

Add your comments about this article : Your username or Email:
CAPTCHA

Send email to the article author


Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

© 2024 CC BY-NC 4.0 | Mathematical Researches

Designed & Developed by : Yektaweb