Geodesic
A generalized notion of $n$-weak amenability
Mathematica Bohemica, Tome 139 (2014) no. 1, pp. 99-112

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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 $L^1(G)$.
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 $L^1(G)$.
DOI : 10.21136/MB.2014.143639
Classification : 22D15, 43A10, 43A20, 46H25
Keywords: Banach algebra; continuous homomorphism; $(\varphi, \psi )$-derivation; $n$-weak amenability 
Bodaghi, Abasalt; Shojaee, Behrouz. A generalized notion of $n$-weak amenability. Mathematica Bohemica, Tome 139 (2014) no. 1, pp. 99-112. doi: 10.21136/MB.2014.143639
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