Remarks on separation of convex sets, fixed-point theorem, and applications in theory of linear operators (Q2472291)

In the first part of the paper the author obtains two separation theorems for two disjoint convex sets in a strictly convex reflexive Banach space. Next he establishes certain conditions under which a continuous linear operator acting in a reflexive Banach space has an eigenvector. Finally, a result about existence of an invariant subspace of a linear bounded operator is given.