Self-Adjoint Extensions of Bipartite Hamiltonians

We compute the deficiency spaces of operators of the form $H_A{\hat{\otimes}} I + I{\hat{\otimes}} H_B$,forsymmetric$H_A$andself-adjoint$H_B$. 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 by Ibort, Marmo and P'erez-Pardo, but only proven under the restriction of $H_B$ having discrete, non-degenerate spectrum.