A Kadison transitivity theorem for C*-semigroups

摘要

We prove a semigroup analogue of the Kadison Transitivity Theorem for C*-algebras. Specifically, we show that a closed, homogeneous, self-adjoint, topologically transitive, semigroup of operators acting on a separable Hilbert space is (strictly) transitive if the semigroup contains a non-zero compact operator. Additional structural information about such semigroups is obtained, and examples are provided to demonstrate that the theorem is the best possible in the semigroup case. (c) 2007 Elsevier Inc. All rights reserved.