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

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A Result on the diagonal of contractible operator Banach algebras
Maysam Maysami Sadr
Department of Mathematics , sadr@iasbs.ac.ir
Abstract:   (372 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 A⊗πA 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.
 
Keywords: Banach algebra, contractibility, diagonal, algebra of bounded linear operators, amenability.
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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
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