Vadim Kostrykin
Concavity of Eigenvalue Sums and The Spectral Shift Function
(36K, LaTeX 2e)

ABSTRACT.  It is well known that the sum of negative (positive) eigenvalues of some finite 
Hermitian matrix $V$ is concave (convex) with respect to $V$. Using the theory 
of the spectral shift function we generalize this property to self-adjoint 
operators on separable Hilbert space with an arbitrary spectrum. More 
precisely, we prove that the spectral shift function integrated with respect to 
the spectral parameter from $-\infty$ to $\lambda$ (from $\lambda$ to 
$+\infty$) is concave (convex) with respect to trace class perturbations. The 
case of relative trace class perturbations is also considered.