Criterion for the symmetry of a spectrum (Q960676)

The main result of the paper under review characterizes a nuclear operator \(A\) acting in a separable Hilbert space with a central-symmetric spectrum by the condition that \(\text{tr}\, A^{2n-1}=0\), \(n\in \mathbb{N}\). This symmetry criterion, like the correspondent example, is presented by the author in connection with a problem of optimal control.