Integral Equations and Operator Theory

, Volume 36, Issue 4, pp 480–498 | Cite as

Quadratically hyponormal weighted shifts and their examples

  • Il Bong Jung
  • Sang Soo Park


We discuss some characterizations for the quadratical hyponormal unilateral weighted shiftWα with a weight sequence α, which give a distinction example for quadratical hyponormality and positively quadratical hyponormality. In addition, we consider a recursively quadratically hyponormal weighted shift with a recursive weight α: {ie480-1} which is a back step extension of subnormal completion ofu,v, andw with0<x<-u<v<w, and prove that the recursively weighted shiftWα is quadratically hyponormal if and only if it is positively quadratically hyponormal.

1991 Mathematics Subject Classification

47B37 47B20 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Ch] Y. Choi,A propagation of quadratically hyponormal weighted shifts, submitted.Google Scholar
  2. [Cu1] R. Curto,Quadratically hyponormal weighted shifts Integral Equations and Operator Theory13 (1990), 49–66.Google Scholar
  3. [Cu2] R. Curto,Joint hyponormality: A bridge between hyponormality and subnormality, Proc. Symposia Pure Math.51 (1990), 69–91.Google Scholar
  4. [CuF1] R. Curto and L. Fialkow,Recursively generated weighted shifts and the subnormal completion problem, Integral Equations and Operator Theory17 (1993), 202–246.Google Scholar
  5. [CuF2] R. Curto and L. Fialkow,Recursively generated weighted shifts and the subnormal completion problem, II, Integral Equations and Operator Theory18, (1994), 369–426.Google Scholar
  6. [CuJ] R. Curto and I. Jung,Quadratically hyponormal weighted shifts with first two equal weights, Integral Equations and Operator Theory, to appear.Google Scholar
  7. [CuP1] R. Curto and M. Putinar,Existence of non-subnormal polynomially hyponormal operators, Bull. Amer. Math. Soc.25 (1991), 373–378.Google Scholar
  8. [CuP2] R. Curto and M. Putinar,Nearly subnormal operators and moment problems, J. Functional Analysis115 (1993), 480–497.Google Scholar
  9. [Sta] J. Stampfli,Which weighted shifts are subnormal, Pacific J. Math.17, (1996), 367–379.Google Scholar
  10. [Wol] Wolfram Research, Version 3.0, Wolfram Research Inc., Champaign, IL, (1996).Google Scholar

Copyright information

© Birkhäuser Verlag 2000

Authors and Affiliations

  • Il Bong Jung
    • 1
  • Sang Soo Park
    • 1
  1. 1.Department of Mathematics College of Natural SciencesKyungpook National UniversityTaeguKorea

Personalised recommendations