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Integral Equations and Operator Theory

, Volume 73, Issue 1, pp 93–106 | Cite as

On Semi-weakly n-Hyponormal Weighted Shifts

  • Younghae Do
  • George Exner
  • Il Bong JungEmail author
  • Chunji Li
Article

Abstract

Semi-weak n-hyponormality is defined and studied using the notion of positive determinant partition. Several examples related to semi-weakly n-hyponormal weighted shifts are discussed. In particular, it is proved that there exists a semi-weakly three-hyponormal weighted shift W α with α 0 = α 1 < α 2 which is not two-hyponormal, which illustrates the gaps between various weak subnormalities.

Mathematics Subject Classification

47B20 47B37 

Keywords

Hyponormal operators quadratically hyponormal operators polynomially hyponormal operators weakly n-hyponormal operators 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Younghae Do
    • 1
  • George Exner
    • 2
  • Il Bong Jung
    • 1
    Email author
  • Chunji Li
    • 3
  1. 1.Department of MathematicsKyungpook National UniversityDaeguKorea
  2. 2.Department of MathematicsBucknell UniversityLewisburgUSA
  3. 3.Institute of System ScienceNortheastern UniversityShenyangPeople’s Republic of China

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