Abstract.
In this paper we give a new proof of the existence of disintegration measures using the Hausdorff Moment Problem on a Borel measurable space X × Y, where X ≡ Y is the unit interval. Using this new tool, we can give an abstract solution, moreover, and a concrete necessary condition for the Lifting Problem for contractive 2-variable weighted shifts. In addition, we have a new, computable, and sufficient condition for the Lifting Problem for 2-variable weighted shifts, and an improved version of the Curto-Muhly-Xia conjecture [8] for 2-variable weighted shifts.
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Yoon, J. Disintegration of Measures and Contractive 2-Variable Weighted Shifts. Integr. equ. oper. theory 59, 281–298 (2007). https://doi.org/10.1007/s00020-007-1509-x
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DOI: https://doi.org/10.1007/s00020-007-1509-x