Self-adjoint extensions of bipartite Hamiltonians

We compute the deficiency spaces of operators of the form ⊗̂ +⊗̂ , for symmetric and self-adjoint . This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301], but only proven under the restriction of having discrete, non-degenerate spectrum