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# Journal of Operator Theory

Volume 38, Issue 2, Fall 1997  pp. 265-296.

On the contractions in the classes $\mathbb A_{m,n}$

Authors Isabelle Chalendar (1) and Frederic Jaeck (2)
Author institution: (1) UFR Mathematiques et Informatique, Universite Bordeaux I, 351, cours de la Liberation, 33405 Talence Cedex, FRANCE. E-mail: chalenda@math.u-bordeaux.fr
(2) UFR Mathematiques et Informatique, Universite Bordeaux I, 351, cours de la Liberation, 33405 Talence Cedex, FRANCE. E-mail: jaeck@math.u-bordeaux.fr

Summary:  Let T be a contraction in the class $\mathbb A$ acting on a Hilbert space. Sufficient conditions in terms of the multiplicity of certain natural unitary operators associated with the $C_{0\cdot}$, $C_{\cdot 0}$, $C_{1\cdot}$ or $C_{\cdot 1}$ part of T are given to ensure that T belongs to the class $\mathbb A_{n,m}, n, m \in \mathbb N*$. Along the way we obtain new relations between the boundary sets involved in arbitrary triangulations of T.

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