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DISINTEGRATION-OF-MEASURE TECHNIQUES FOR COMMUTING MULTIVARIABLE WEIGHTED SHIFTS

Published online by Cambridge University Press:  20 February 2006

RAÚL E. CURTO  and
JASANG YOON
RAÚL E. CURTO
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, IO 52242, USArcurto@math.uiowa.edu, http://www.math.uiowa.edu/~rcurto/
JASANG YOON
Affiliation:
Department of Mathematics, Iowa State University, Ames, IO 50011, USAjyoon@iastate.edu, http://www.public.iastate.edu/~jyoon/
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Abstract

We employ techniques from the theory of disintegration of measures to study the Lifting Problem for commuting $n$-tuples of subnormal weighted shifts. We obtain a new necessary condition for the existence of a lifting, and generate new pathology associated with bringing together the Berger measures associated to each individual weighted shift. For subnormal $2$-variable weighted shifts, we then find the precise relation between the Berger measure of the pair and the Berger measures of the shifts associated to horizontal rows and vertical columns of weights.

Keywords

47B2047B3747A1328A50 (primary)44A6047-0447A20 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 92 , Issue 2 , March 2006 , pp. 381 - 402
Copyright
2006 London Mathematical Society

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Footnotes

Research partially supported by NSF Grants DMS-0099357 and DMS-0400741.