Let \(\mathcal {H}\) be a separable Hilbert space and \(\mathcal {L}_{0}\subset \mathcal {B}(\mathcal {H})\) a complete reflexive lattice. We construct a class of subspace lattices \(\mathcal {L}\) on the direct sum \(\mathcal {K}=\mathcal {H}^{(n_0)}\) of \(n_0\ge 3\) copies of \(\mathcal {H}\) from \(\mathcal {L}_{0}\) . Let \({\textrm{Alg}}\mathcal {L}\) be the corresponding subspace lattice algebras. We first show that \({\textrm{Alg}}\mathcal {L}\) is decomposable if and only if \({\textrm{Alg}}\mathcal {L}_{0}\) is decomposable. Then we show that an operator T in \({\textrm{Alg}}\mathcal {L}\) is single if and only if T is of rank 1 under certain conditions. Finally, under certain conditions, we prove that every linear derivation on \({\textrm{Alg}}\mathcal {L}\) is automatically continuous and that every bounded local derivation on \({\textrm{Alg}}\mathcal {L}\) is a derivation.
