Abstract
We study the problem of determining which bounded linear operator on a Hilbert space can be dilated to a singular unitary operator. Some of the partial results we obtained are (1) every strict contraction has a diagonal unitary dilation, (2) everyC 0 contraction has a singular unitary dilation, and (3) a contraction with one of its defect indices finite has a singular unitary dilation if and only if it is the direct sum of a singular unitary operator and aC 0(N) contraction. Such results display a scenario which is in marked contrast to that of the classical case where we have the absolute continuity of the minimal unitary power dilation of any completely nonunitary contraction.
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Wu, P.Y., Takahashi, K. Singular unitary dilations. Integr equ oper theory 33, 231–247 (1999). https://doi.org/10.1007/BF01233966
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DOI: https://doi.org/10.1007/BF01233966