Bounds for eigenvalue sums of Schrödinger operators with complex radial potentials

<p dir="ltr">We consider eigenvalue sums of Schrödinger operators −Δ+<i>V </i>on <i>L</i>²(R^d) with complex radial potentials <i>V </i>∈ <i>L</i>q(R^d), <i>q</i> < <i>d</i>. We prove quantitative bounds on the distribution of the eigenvalues in terms of the <i>L</i>^<em>q</em> norm of <i>V. </i>A consequence of our bounds is that, if the eigenvalues (<i>z</i>_<em>j</em>_​) accumulate to a point in (0,∞), then (Im<i>z</i>_j)is summable. The key technical tools are resolvent estimates in Schatten spaces. We show that these resolvent estimates follow from spectral measure estimates by an epsilon removal argument.</p>