Weak Amenability of Banach Algebra-Valued \(\ell _p\)-Sequence Algebras

We characterize weak amenability of Banach algebras of the form \(c_0(A)\) $c_0(A)$ and \(\ell _p(A)\) ${\ell }_p(A)$ , where A is an arbitrary Banach algebra and \(1\leqslant p<\infty \) $1⩽p<\infty$ . Specifically, we generalize the case of \(\ell _1(A)\) ${\ell }_1(A)$ for a \(C^*\) $C^{\ast }$ -algebra A. We also discuss amenability and contractibility of these algebras.