Self-adjoint extensions of bipartite Hamiltonians

Abstract We compute the deficiency spaces of operators form $H_A{\hat {\otimes }} I + I{\hat H_B$ , for symmetric $H_A$ and self-adjoint $H_B$ . This enables us to construct extensions (if they exist) by means von Neumann's theory. The structure 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 restriction having discrete, non-degenerate spectrum.