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C ·0 CONTRACTIONS: DUAL OPERATOR ALGEBRAS, JORDAN MODELS AND MULTIPLICITY

GEORGE R. EXNER, YOUNG SOO JO and IL BONG JUNG
Journal of Operator Theory
Vol. 33, No. 2 (Spring 1995), pp. 381-394
Published by: Theta Foundation
Stable URL: http://www.jstor.org/stable/24714919
Page Count: 14
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C
          ·0
          CONTRACTIONS: DUAL OPERATOR ALGEBRAS, JORDAN MODELS AND MULTIPLICITY
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Abstract

We discuss contraction operators T in the class C·0∩A with defect index dT < ∞, where 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 ${\mathrm{A}}_{\mathrm{n},{\mathrm{\aleph }}_{0}}$ 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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