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Proper Contractions and Invariant Subspaces

  • Author(s): Kubrusly, Carlos S
  • Levan, Nhan
  • et al.
Abstract

Let T be a contraction and let A be the strong limit of \ {T^{*n}T^{n}\}_{n\geq 1}. We prove the following theorem. If a hyponormal contraction T does not have any nontrivial invariant subspace, then T is either a proper contraction of class C_{00} or a nonstrict proper contraction of class C_{10} for which A is a completely nonprojective nonstrict proper contraction. Moreover, its self-commutator [T^{*}, T] is a strict contraction.

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