We compute the deficiency spaces of operators of the form
$H_A{\hat {\otimes }} I + I{\hat {\otimes }} H_B$
, for symmetric
$H_A$
and self-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 in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor.47(38) (2014) 385301], but only proven under the restriction of
$H_B$
having discrete, non-degenerate spectrum.
We compute the deficiency spaces of operators of the form H A ⊗I + I ⊗H B , for symmetric H A and self-adjoint H B . This enables us to construct selfadjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in [IMPP14], but only proven under the restriction of H B having discrete, non-degenerate spectrum.
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