Published 2011-03-10
Keywords
- amenability,
- approximate amenability,
- \(\ell^1\)-Munn algebra
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How to Cite
Approximate Amenability of Matrix Algebras. (2011). Scientia Series A: Mathematical Sciences, 21, 17-24. https://revistas.usm.cl/scientia/article/view/163
Abstract
In this paper, we study approximate amenability of matrix algebras. We show that every derivation from \(M_n(\mathcal{A})\) into \(M_n(E^{(m)})\) is the sum of an inner derivation and a derivation induced by a derivation from \(\mathcal{A}\) into \(E^{(m)}\), where \(\mathcal{A}\) is a Banach algebra and \(E\) is a Banach \(\mathcal{A}\)-bimodule. By using this, we provide many results in approximate and permanent weak amenability of these algebras.
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