6533b870fe1ef96bd12cfa1e

RESEARCH PRODUCT

Quasi-isometries associated to A-contractions

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Abstract Given two operators A and T ( A ≥ 0 , ‖ A ‖ = 1 ) on a Hilbert space H satisfying T ⁎ A T ≤ A , we study the maximum subspace of H which reduces M = A 1 / 2 T to a quasi-isometry, that is on which the equality M ⁎ M = M ⁎ 2 M 2 holds. In some cases, this subspace coincides with the maximum subspace which reduces M to a normal partial isometry, for example when A = T T ⁎ , 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 − A 2 . 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.