Dynamical systems and complex networks: A Koopman operator perspective

The uploaded paper is a perspective/review that defines the transfer operators and notes when they are self-adjoint, but it does not state or prove the trace bounds on joint metastability the model solves. The model’s proof is essentially correct once a crucial missing hypothesis is added: T must be compact and self-adjoint (e.g., reversible dynamics with µ equal to the invariant density), which the paper explains is the case under detailed balance. Without explicitly assuming self-adjointness, the model’s use of the spectral theorem and Ky Fan’s principle is not justified.