Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THE PROPAGATION PHENOMENON OF WEIGHTED SHIFTS

  • Kim, An-Hyun (Department of Mathematics, Changwon National University) ;
  • Kwon, Eun-Young (Educational institute of engineering, Changwon National University)
  • Published : 2010.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

This paper concerns the propagation phenomenon of weighted shifts. We here establish the existence of positive real numbers b and c (1 < b < c) such that the recursive weighted shift $W_{1,(1,\sqrt{b}\sqrt{c})$^ is quadratically but not cubically hyponormal.

Keywords

References

  1. A. Athavale, On joint hyponormality of operators, Proc. Amer. Math. Soc. 103 (1988), no. 2, 417–423. https://doi.org/10.2307/2047154
  2. Y. B. Choi, A propagation of quadratically hyponormal weighted shifts, Bull. Korean Math. Soc. 37 (2000), no. 2, 347–352.
  3. Y. B. Choi, J. K. Han, and W. Y. Lee, One-step extension of the Bergman shift, Proc. Amer. Math. Soc. 128 (2000), no. 12, 3639–3646. https://doi.org/10.1090/S0002-9939-00-05516-7
  4. J. B. Conway, The Theory of Subnormal Operators, Math. Surveys and Monographs, vol. 36, Amer. Math. Soc., Providence, 1991.
  5. J. B. Conway and W. Szymanski, Linear combinations of hyponormal operators, Rocky Mountain J. Math. 18 (1988), no. 3, 695–705. https://doi.org/10.1216/RMJ-1988-18-3-695
  6. R. E. Curto, Quadratically hyponormal weighted shifts, Integral Equations Operator Theory 13 (1990), no. 1, 49–66. https://doi.org/10.1007/BF01195292
  7. R. E. Curto, An operator-theoretic approach to truncated moment problems, Linear operators (Warsaw, 1994), 75–104, Banach Center Publ., 38, Polish Acad. Sci., Warsaw, 1997. https://doi.org/10.4064/-38-1-75-104
  8. R. E. Curto and L. A. Fialkow, Recursively generated weighted shifts and the subnormal completion problem. II, Integral Equations Operator Theory 18 (1994), no. 4, 369–426. https://doi.org/10.1007/BF01200183
  9. R. E. Curto and I. B. Jung, Quadratically hyponormal weighted shifts with two equal weights, Integral Equations Operator Theory 37 (2000), no. 2, 208–231. https://doi.org/10.1007/BF01192423
  10. R. E. Curto and W. Y. Lee, Joint hyponormality of Toeplitz pairs, Mem. Amer. Math. Soc. 150 (2001), no. 712, x+65 pp.
  11. R. E. Curto, P. S. Muhly, and J. Xia, Hyponormal pairs of commuting operators, Contributions to operator theory and its applications (Mesa, AZ, 1987), 1–22, Oper. Theory Adv. Appl., 35, Birkhauser, Basel, 1988.
  12. P. Fan, A note on hyponormal weighted shifts, Proc. Amer. Math. Soc. 92 (1984), no. 2, 271–272. https://doi.org/10.2307/2045200
  13. A. Joshi, Hyponormal polynomials of monotone shifts, Indian J. Pure Appl. Math. 6 (1975), no. 6, 681–686.
  14. I. B. Jung and S. S. Park, Quadratically hyponormal weighted shifts and their examples, Integral Equations Operator Theory 36 (2000), no. 4, 480–498. https://doi.org/10.1007/BF01232741
  15. J. Stampfli, Which weighted shifts are subnormal?, Pacific J. Math. 17 (1966), 367–379. https://doi.org/10.2140/pjm.1966.17.367