DOI QR코드

DOI QR Code

Weakly Hyponormal Composition Operators and Embry Condition

Lee, Mi-Ryeong;Park, Jung-Woi

  • Received : 2009.01.05
  • Accepted : 2009.05.04
  • Published : 2009.12.31

Abstract

We investigate the gaps among classes of weakly hyponormal composition operators induced by Embry characterization for the subnormality. The relationship between subnormality and weak hyponormality will be discussed in a version of composition operator induced by a non-singular measurable transformation.

Keywords

subnormal;n-hyponormal;E(n)-hyponormal;composition operator

References

  1. J. Bram, Subnormal operators, Duke Math. J., 22(1955), 75-94. https://doi.org/10.1215/S0012-7094-55-02207-9
  2. C. Burnap and I. B. Jung, Composition operators with weak hyponormality, J. Math. Anal. Appl., 337(2008), 686-694. https://doi.org/10.1016/j.jmaa.2007.02.082
  3. C. Burnap, I. B. Jung and A. Lambert, Separating partial normality classes with composition operators, J. Operator Theory, 53(2005), 381-397.
  4. M. Embry, A generalization of the Halmos-Bram condition for subnormality, Acta. Sci. Math.(Szeged), 35(1973), 61-64.
  5. J. Conway, Subnormal Operators, Pitman Advanced Publishing Program, 1981.
  6. R. E. Curto and L. A. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Integral Equation and Operator Theory, 17(1993), 202-246. https://doi.org/10.1007/BF01200218
  7. I. Jung, M. Lee and S. Park, Separating classes of composition operators via subnormal condition, Proc. Amer. Math. Soc., 135(2007), 3955-3965. https://doi.org/10.1090/S0002-9939-07-09003-X
  8. J. W. Park and S. S. Park, On k-hyponormal weighted translation semigroups, Bull. Kor. Math. Soc., 39(2002), 527-534. https://doi.org/10.4134/BKMS.2002.39.4.527
  9. S. McCullough and V. I. Paulsen, A note on joint hyponormality, Proc. Amer. Math. Soc., 107(1989), 187-195. https://doi.org/10.1090/S0002-9939-1989-0972236-8
  10. S. McCullough and V. I. Paulsen, k-hyponormality of weighted shifts, Proc. Amer. Math. Soc., 116(1992), 165-169.
  11. Wolfram Research, Inc. Mathematica, Version 3.0, Wolfram Reseqrch Inc. Champaign, IL, 1996.

Cited by

  1. Weak Hyponomal Composition Operators Induced by a Tree vol.50, pp.1, 2010, https://doi.org/10.5666/KMJ.2010.50.1.089