Journal of Operator Theory

Volume 33, Issue 2, Spring 1995 pp. 381-394.

$C_{\cdot 0}$ contractions: dual operator algebras, Jordan models, and multiplicity

Authors: George R. Exner (1), Young Soo Jo (2) and Il Bong Jung (3)
Author institution: (1) Department of Mathematics, Bucknell University, Lewisburg, PA 17837, U.S.A.
(2) Department of Mathematics, Keimyung University, Taegu, 704-200, KOREA
(3) Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu, 702-701, KOREA

Summary: We discuss contraction operators T in the class

$C_{\cdot 0} \cap \mathbb A$ with defect index

$d_T < \infty$ , where

$\mathbb A$ is the class of absolutely continuous contractions for which the Sz.-Nagy-FoiaÅŸ, functional calculus is an isometry. We show that these form particularly nice representatives of the classes

$\mathbb A_{n,\aleph_0}$ since their membership is completely determined by the multiplicity of either the shift piece of their Jordan model or the unitary piece of their minimal coisometric extension.

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