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.

中文翻译：

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二部哈密顿量的自伴随扩展

我们计算以下形式的运算符的缺陷空间$H_A{\hat {\otimes }} I + I{\hat {\otimes }} H_B$, 对于对称$H_A$和自伴$H_B$. 这使我们能够通过冯诺依曼的理论构造自伴随扩展（如果它们存在的话）。Ibort 等人已经断言了这种情况下缺陷空间的结构。[边界动力学驱动的纠缠，J.物理。答：数学。理论。47(38) (2014) 385301]，但仅在以下限制条件下证明$H_B$具有离散的、非退化的频谱。