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Curvature Invariant and Generalized Canonical Operator Models – I

  • Ronald G. DouglasEmail author
  • Yun-Su Kim
  • Hyun-Kyoung Kwon
  • Jaydeb Sarkar
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 221)

Abstract

One can view contraction operators given by a canonical model of Sz.-Nagy and Foias as being defined by a quotient module where the basic building blocks are Hardy spaces.I n this note we generalize this framework to allow the Bergman and weighted Bergman spaces as building blocks, but restricting attention to the case in which the operator obtained is in the Cowen-Douglas class and requiring the multiplicity to be one.W e view the classification of such operators in the context of complex geometry and obtain a complete classification up to unitary equivalence of them in terms of their associated vector bundles and their curvatures.

Keywords

Cowen-Douglas class Sz.-Nagy-Foias model operator curvature resolutions of Hilbert modules 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  • Ronald G. Douglas
    • 1
    Email author
  • Yun-Su Kim
    • 2
  • Hyun-Kyoung Kwon
    • 3
  • Jaydeb Sarkar
    • 4
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.Department of MathematicsThe University of ToledoToledoUSA
  3. 3.Department of Mathematical SciencesSeoul National UniversitySeoulRepublic of Korea
  4. 4.Statistic and Mathematics UnitIndian Statistical InstituteBangaloreIndia

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