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A NOTE ON CUBICALLY HYPONORMAL WEIGHTED SHIFTS

  • Li, Chunji ;
  • Cho, Muneo ;
  • Lee, Mi Ryeong
  • Received : 2013.08.11
  • Published : 2014.07.31

Abstract

In this paper, we show that any cubically hyponormal weighted shift with first two equal weights is flat. And we give an example of a weighted shift which is not cubically hyponormal but almost-cubically hyponormal.

Keywords

weighted shift;cubically hyponormal operator;flatness

References

  1. R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal com-pletion problem, Integ. Equ. Oper. Theory 17 (1993), no. 2, 202-246. https://doi.org/10.1007/BF01200218
  2. R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem. II, Integ. Equ. Oper. Theory 18 (1994), no. 4, 369-426. https://doi.org/10.1007/BF01200183
  3. Y. Do, G. Exner, I. Jung, and C. Li, On semi-weakly n-hyponormal weighted shifts, Integ. Equ. Oper. Theory 73 (2012), no. 1, 93-106. https://doi.org/10.1007/s00020-012-1960-1
  4. I. Jung and S. Park, Cubically hyponormal weighted shifts and their examples, J. Math. Anal. Appl. 247 (2000), no. 2, 557-569. https://doi.org/10.1006/jmaa.2000.6879
  5. J. Stampfli, Which weighted shifts are subnormal, Pacific J. Math. 17 (1966), 367-379. https://doi.org/10.2140/pjm.1966.17.367
  6. Wolfram Research, Inc. Mathematica, Version 8.0, Wolfram Research, Champaign, 2010.
  7. R. Curto and I. Jung, Quadratically hyponormal weighted shifts with two equal weights, Integ. Equ. Oper. Theory 37 (2000), no. 2, 208-231. https://doi.org/10.1007/BF01192423
  8. R. Curto and M. Putinar, Nearly subnormal operators and moment problems, J. Funct. Anal. 115 (1993), no. 2, 480-497. https://doi.org/10.1006/jfan.1993.1101
  9. Y. Choi, A propagation of quadratically hyponormal weighted shifts, Bull. Korean Math. Soc. 37 (2000), no. 2, 347-352.
  10. R. Curto, Quadratically hyponormal weighted shifts, Integ. Equ. Oper. Theory 13 (1990), no. 1, 49-66. https://doi.org/10.1007/BF01195292

Cited by

  1. Semi-cubic Hyponormality of Weighted Shifts with Stampfli Recursive Tail vol.88, pp.2, 2017, https://doi.org/10.1007/s00020-017-2373-y
  2. On Semi-cubically Hyponormal Weighted Shifts with First Two Equal Weights vol.56, pp.3, 2016, https://doi.org/10.5666/KMJ.2016.56.3.899
  3. On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights vol.7, pp.2, 2019, https://doi.org/10.3390/math7020212

Acknowledgement

Supported by : National Science Foundation of China