Abstract

Let (H, [.,.]) be a Hilbert space, and F: H --> H be an operator with closed convex values. Denote by sigma (F) the set of all (real) eigenvalues of F. As shown in this note, if F satisfies a so-called upper-normality assumption, then it is possible to derive a simple variational formula for the supremum of sigma (F). Lower-normality of F yields, of course, an analogous formula for the infimum of sigma (F).