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 $\mathbf{B(H)}$ which contains $alg\mathcal{L}$ and
$\phi$ 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.