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Quasi-isometries associated to A-contractions

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Identifiers
DOI: 10.1016/j.laa.2014.07.016
Keywords
  • Partial Isometry
  • Quasi-Isometry
  • Hyponormal Operator
  • Invariant Subspace

Abstract

Abstract Given two operators A and T (A≥0, ‖A‖=1) on a Hilbert space H satisfying T⁎AT≤A, we study the maximum subspace of H which reduces M=A1/2T to a quasi-isometry, that is on which the equality M⁎M=M⁎2M2 holds. In some cases, this subspace coincides with the maximum subspace which reduces M to a normal partial isometry, for example when A=TT⁎, and in particular if T⁎ is a cohyponormal contraction. In this case the corresponding subspace can be completely described in terms of asymptotic limit of the contraction T. When M is quasinormal and M⁎M=A then the former above quoted subspace reduces to the kernel of A−A2. The case of an arbitrary contraction (or particularly, of a partial isometry) is also considered, for which we completely describe the reducing (quasi)-isometric part, as well as the invariant quasi-isometric part.

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