A trace formula for Hankel operators

Abstract:

We show that if $G$ is an operator valued analytic function in the open right half plane such that the Hankel operator $H_G$ with symbol $G$ is of trace-class, then $G$ has continuous extension to the imaginary axis, \[ G(\infty ):=\lim \limits _{r \rightarrow \infty \atop r \in \mathcal {R}} G(r)\] exists in the trace-class norm, and $\mathrm {tr}(H_G)={1\over 2} \mathrm {tr}(G(0)-G(\infty ))$.