Abstract

A Lidskii theorem is a valuable tool for understanding the connection between the trace of the operator and its eigenvalues in the Hilbert space. In this article, we extend the definition of the trace class to the operators on the separable reflexive Banach spaces and generalize the Lidskii theorem to the trace class in the separable reflexive Banach spaces. Also, we consider the Fredholm theory on the trace class and establish the formula  which establishes a new exponential identity.

Keywords

Reflexive Banach space; Finite rank operator; Trace class; Trace operator; Spectral theory; Gaussian distribution; Hahn-Banach theorem

Introduction