In this paper we introduce the notion of $\varphi$-commutativity for a Banach algebra $A$, where $\varphi$ is a continuous homomorphism on $A$ and study the concept of $\varphi$-weak amenability for $\varphi$-commutative Banach algebras. We give an example to show that the class of $\varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We characterize $\varphi$-weak amenability of $\varphi$-commutative Banach algebras and prove some hereditary properties. Moreover we verify some of the previous available results about commutative weakly amenable Banach algebras, for $\varphi$-commutative $\varphi$-weakly amenable Banach algebras.
Sadeghi,H and Lashkarizadeh,M . (2018). Homomorphism Weak amenability of certain Banach algebras. International Journal of Nonlinear Analysis and Applications, 9(1), 235-245. doi: 10.22075/ijnaa.2018.1201.1276
MLA
Sadeghi,H , and Lashkarizadeh,M . "Homomorphism Weak amenability of certain Banach algebras", International Journal of Nonlinear Analysis and Applications, 9, 1, 2018, 235-245. doi: 10.22075/ijnaa.2018.1201.1276
HARVARD
Sadeghi H, Lashkarizadeh M. (2018). 'Homomorphism Weak amenability of certain Banach algebras', International Journal of Nonlinear Analysis and Applications, 9(1), pp. 235-245. doi: 10.22075/ijnaa.2018.1201.1276
CHICAGO
H Sadeghi and M Lashkarizadeh, "Homomorphism Weak amenability of certain Banach algebras," International Journal of Nonlinear Analysis and Applications, 9 1 (2018): 235-245, doi: 10.22075/ijnaa.2018.1201.1276
VANCOUVER
Sadeghi H, Lashkarizadeh M. Homomorphism Weak amenability of certain Banach algebras. IJNAA. 2018;9(1):235-245. doi: 10.22075/ijnaa.2018.1201.1276
International Journal of Nonlinear Analysis and Applications