Derivations and local derivations on strongly double triangle subspace lattice algebras

Let [image omitted] be a strongly double triangle subspace lattice. It is proved that a derivation from [image omitted] into [image omitted] is quasi-spatial. It is also shown that if is derivable at zero, i.e. if (A)B + A(B) = 0 for all A and B in [image omitted] with AB = 0, then (A) = (A) + A for all [image omitted] where is a derivation and is a scalar. It is also shown that a local derivation from [image omitted] into [image omitted] is a derivation.