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 Frédéric Jaeck (2)
Author institution:(1) UFR Mathématiques et Informatique, Université Bordeaux I, 351, cours de la Libération, 33405 Talence Cedex, FRANCE. E-mail: chalenda@math.u-bordeaux.fr
(2) UFR Mathématiques et Informatique, Université Bordeaux I, 351, cours de la Libération, 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.

Keywords: Hilbert space, absolutely continuous contraction, dual operator algebra, minimal coisometric extension, minimal isometric dilation.

Contents Full-Text PDF