A PROPAGATION OF QUADRATICALLY HYPONORMAL WEIGHTED SHIFTS

  • Choi, Yong-Bin (Department of Mathematics Sungkyunkwan University)
  • Published : 2000.05.01

Abstract

In this note we answer to a question of Curto: Non-first two equal weights in the weighted shift force subnormality in the presence of quadratic hyponormality. Also it is shown that every hyponormal weighted shift with two equal weights cannot be polynomially hyponormal without being flat.

Keywords

Quadratically hyponormal operators;polynomially hyponormal operators;weighted shifts;propagations

References

  1. Proc. Amer. Math. Soc. v.103 On hyponormality of operators A. Athavale
  2. Int. Eq. Op. Th v.18 Recursively generated weighted shifts and the subnormal completion problem R.E. Curto;L.A. Fialkow
  3. Duke Math. J. v.22 Subnormal operators J. Bram
  4. Int. Eq. Op. Th v.13 Quadratically hyponormal weighted shifts R.E. Curto
  5. Pacific J. Math. v.17 Which weighted shift are subnormal J. Stampfli
  6. Operator Th: Adv. Appl. v.35 Hyponormal pairs of commuting operators R.E. Curto;P. Muhly;J. Xia
  7. Research Notes in Mathematics v.51 Subnormal Operators J.B. Conway