Approximate Amenability of Matrix Algebras - A. Jabbari; H. Hossein Zadeh (Scientia, 2025)
In this paper, we study approximate amenability of matrix algebras. We show that every derivation from \(M_n(A)\) into \(M_n(E^(m))\) is the sum of an inner derivation and a derivation induced by a derivation from \(A\) into \(E^(m)\), where \(A\) is a Banach algebra and \(E\) is a Banach \(A\)-bimodule. By using this, we provide many results in approximate and permanent weak amenability of these algebras.