2013/01/25 by Sophie Grivaux, Grivaux, Sophie, Maria Roginskaya +1
Mathematics · #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Holomorphic and Operator Theory #math.DS #math.FA
paper · pdf · doi:10.48550/arxiv.1301.6144
10 p
arxiv created 2013/01/25 · openalex publication_date 2013/01/25 · arxiv updated 2013/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Invariant Subset Problem on the Hilbert space is to know whether there exists a bounded linear operator T on a separable infinite-dimensional Hilbert space H such that the orbit \Tnx; n≥ 0\ of every non-zero vector x∈ H under the action of T is dense in H. We show that there exists a bounded linear operator T on a complex separable infinite-dimensional Hilbert space H and a unitary operator V on H, such that the following property holds true: for every non-zero vector x∈ H, either x or Vx has a dense orbit under the action of T. As a consequence, we obtain in particular that there exists a minimal action of the free semi-group with two generators \F+2 on a complex separable infinite-dimensional Hilbert space H.