The spectral theorem and von Neumann algebras
Orr Moshe Shalit · 2025
In this chapter we shall prove the spectral theorem for normal operators on a Hilbert space. The spectral theorem is a cornerstone of operator theory and functional analysis. We shall also use the spectral theorem as a natural link into a brief study of von Neumann algebras, which constitute a special class of C*-algebras that provide a suitable framework for the analysis of normal operators. Von Neumann&s;s double commutant theorem is presented and proved to give a taste of the flavor of von Neumann algebras.