Journal of Operator Theory

Volume 36, Issue 1, Summer 1996 pp. 107-119.

Dual operator algebras and contractions with finite defect indices

Authors: George R. Exner (1) and Il Bong Jung (2)
Author institution:(1) Bucknell University, Lewisburg, PA 17837, USA
(2) Department of Mathematics, College of Natural Science, Kyungpook National University, Taegu 702-701, KOREA

Summary: We characterize the membership in the various dual operator algebra classes $\mathbb A_{m,n}$ of absolutely continuous contraction operators T on Hilbert space with finite defect indices; the characterizations involue multiplicity measures like the difference of the defects or the number of copies of the bilateral shift in the minimal coisometric extension of T. We then give examples of operators in no class $\mathbb A_{m,n}$ with m or n infinite.

Keywords: Dual operator algebra, defect index, minimal coisometric extension.

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