Derivations on FCIN algebras

Abstract

Let $\mathcal{L}$ be an algebra generated by the commuting independent nests, $\mathcal{M}$ is an ultra-weakly closed subalgebra of $\mathbf{B}(\mathbf{H})$ which contains $alg\mathcal{L}$ and $\varphi$ is a norm continuous linear mapping from $alg\mathcal{L}$ into $\mathcal{M}$. In this paper we will show that a norm continuous linear derivable mapping at zero point from $Alg\mathcal{L}$ to $\mathcal{M}$ is a derivation