Finite Double-Norm and Trace-Class Operators on a Hilbert Space

A functional analytic approach to Weyl’s asymptotic formula for the eigenvalues of the Laplace–Beltrami operator \(\Delta _{M}\) on a manifold M is provided by several abstract theorems in which no mention need be made of differential equations. In this chapter we study operators of finite double-norm and trace operators on an abstract Hilbert space X in the framework of Hilbert–Schmidt Kernels.