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-Foiaş, 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.

Keywords: Dual operator algebras, finite defects, Jordan model, multiplicity.

Contents Full-Text PDF