  The 2-hyperreflexivity of Toeplitz-harmonic type subspace generated by an
isometry or a quasinormal operator is shown. The $k$-hyperreflexivity of the
tensor product $\mathcal{S}\otimes \mathcal{V}$ of a $k$-hyperreflexive
decomposable subspace $\mathcal{S}$ and an abelian von Neumann algebra
$\mathcal{V}$ is established.
