Abstract
We show in this paper that for absolutely continuous contractions on Hilbert space with Hilbert-Schmidt defect in the classes C 10, C 1., or C.0, a number of multiplicity measures coincide. These include some involving dual operator algebra class, the size of a zero operator dilated, and the multiplicity of the unitary piece of the minimal coisometric extension. The main ingredient in these results, and another equivalent multiplicity measure, is the n in an “n-fold analytic co-kernel” defined on the unit disk for such an operator.
The authors were partially supported by KOSEF 94-1400-02-01-3 and a travel grant from Bucknell University.
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Exner, G.R., Jung, I.B. (1998). Some Multplicities for Contractions with Hilbert-Schmidt Defect. In: Bercovici, H., Foias, C.I. (eds) Nonselfadjoint Operator Algebras, Operator Theory, and Related Topics. Operator Theory Advances and Applications, vol 104. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8779-3_7
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DOI: https://doi.org/10.1007/978-3-0348-8779-3_7
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