Disintegration-of-measure techniques for commuting multivariable weighted shifts |
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| Authors: | Curto, Raul E. Yoon, Jasang |
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| Affiliation: | Department of Mathematics, The University of Iowa Iowa City, IO 52242, USA rcurto{at}math.uiowa.edu, http://www.math.uiowa.edu/~rcurto/
Department of Mathematics, Iowa State University Ames, IO 50011, USA jyoon{at}iastate.edu, http://www.public.iastate.edu/~jyoon/ |
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| Abstract: | We employ techniques from the theory of disintegration of measuresto study the Lifting Problem for commuting n-tuples of subnormalweighted shifts. We obtain a new necessary condition for theexistence of a lifting, and generate new pathology associatedwith bringing together the Berger measures associated to eachindividual weighted shift. For subnormal 2-variable weightedshifts, we then find the precise relation between the Bergermeasure of the pair and the Berger measures of the shifts associatedto horizontal rows and vertical columns of weights. 2000 MathematicsSubject Classification 47B20, 47B37, 47A13, 28A50 (primary),44A60, 47-04, 47A20 (secondary). |
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