We continue our study of hyperinvariant subspaces for rationally cyclic subnormal operators. We establish a connection between hyperinvariant subspaces and weak-star continuous point evaluations on the commutant. Introduction. Let A be a compact subset of the complex plane C and let R(K) denote the algebra of rational functions with poles off K. For a positive measure p with support in K let R2...

M. Krein proved in [KR48] 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 l1, operators with invariant sets, contractions on Banach lattices, the Invariant Subspace Problem, and von Neumann algebras. M. Krein proved in ...