Abasalt Bodaghi, Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran, e-mail: abasalt.bodaghi@gmail.com; Behrouz Shojaee, Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran, e-mail: shoujaei@kiau.ac.ir
Abstract: In the current work, a new notion of $n$-weak amenability of Banach algebras using homomorphisms, namely $(\varphi,\psi)$-$n$-weak amenability is introduced. Among many other things, some relations between $(\varphi,\psi)$-$n$-weak amenability of a Banach algebra $\mathcal{A}$ and $M_m(\mathcal{A})$, the Banach algebra of $m\times m$ matrices with entries from $\mathcal{A}$, are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra $L^1(G)$ is ($\varphi,\psi$)-$n$-weakly amenable for any bounded homomorphisms $\varphi$ and $\psi$ on $L^1(G)$.
Keywords: Banach algebra; continuous homomorphism; $(\varphi,\psi)$-derivation; $n$-weak amenability
Classification (MSC 2010): 46H25, 43A20, 22D15
Full text available as PDF.
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
