2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65066M. Krein proved in 1948 that if T is a continuous operator on a normed space leaving invariant an open cone, then its adjoint T* has an eigenvector. We present generalizations of this result as well as some applications to C*-algebras, operators on l_1, operators with invariant sets, contractions on Banach lattices, the Invariant Subspace Problem, and von Neumann algebras.To appear in Rocky Mountain J. MathFunctional Analysis46B40, 47B60, 47B65text