We generalize Moore’s nonstandard proof of the Spectral theorem for bounded self-adjoint operators to the case of unbounded operators. The key step is to use a definition of the nonstandard hull of an internally bounded self-adjoint operator due to Raab.

中文翻译：

---

无界自伴随算子的谱定理的非标准证明

我们将摩尔关于有界自伴随算子的谱定理的非标准证明推广到无界算子的情况。关键步骤是使用由 Raab 引起的内部有界自伴随算子的非标准外壳的定义。