DOI QR코드

DOI QR Code

ON THE NORM ATTAINING OPERATORS

  • Lee, Jun Ik (Department of Mathematics Education Sangmyung University)
  • Received : 2012.11.05
  • Accepted : 2012.12.15
  • Published : 2012.12.30

Abstract

In this paper, we show the norm attaining paranormal operators have a nontrivial invariant subspace. Also, we show the norm attaining quadratically hyponormal weighted shift is subnormal.

Keywords

Acknowledgement

Supported by : Sangmyung University

References

  1. A. Athavale, On joint hyponormality of operators, Proc. Amer. Math. Soc. 103 (1988), 417-423. https://doi.org/10.1090/S0002-9939-1988-0943059-X
  2. E. Bishop, and R.R. Phelps, A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc. 67 (1961), 97-98. https://doi.org/10.1090/S0002-9904-1961-10514-4
  3. J. Bram, Subnormal operators, Duke Math. J. 22(1955), 75-94. https://doi.org/10.1215/S0012-7094-55-02207-9
  4. J. Bourgain, On dentability and the Bishop-Phelps property, Israel J. Math. 28 (1977), 265-271. https://doi.org/10.1007/BF02760634
  5. Y. B. Choi, A propagation of quadratically hyponormal weighted shifts, Bull. Korean Math. Soc. 37 (2000), no. 2, 347-352.
  6. J. Conway, The Theory of Subnormal Operators, Math. Surveys Monogr. 36, Amer. Math. Soc., Providence, 1991.
  7. J.B. Conway and W. Szymanski, Linear combinations of hyponormal operators, Rocky Mountain J. Math. 18 (1988), 695-705. https://doi.org/10.1216/RMJ-1988-18-3-695
  8. R.E. Curto, Quadratically hyponormal weighted shifts, Integral Equations Operator Theory, 13 (1990), 49-66. https://doi.org/10.1007/BF01195292
  9. R. Curto, P. Muhly and J. Xia, Hyponormal pairs of commuting operators, Oper. Theory Adv. Appl. 35 (1988), 1-22.
  10. P. Fan, A note on hyponormal weighted shifts, Proc. Amer. Math. Soc. 92 (1984), 271-272. https://doi.org/10.1090/S0002-9939-1984-0754718-2
  11. P.R. Halmos, A Hilbert space problem book, Springer, New York, 1982.
  12. A. Iwanik, Norm attaining operators on Lebesgue spaces, Pacific J. Math. 83 (1979), 381-386. https://doi.org/10.2140/pjm.1979.83.381
  13. J. Johnson, and J. Wolfe, Norm attaining operators, Studia Math. 65 (1979), 7-19. https://doi.org/10.4064/sm-65-1-7-19
  14. A.D. Joshi, An example of a monotone shift which is not quadratically hyponormal, Math. Student 51 (1983), 193-194.
  15. J. Lindenstrauss, On operators which attain their norm, Israel J. Math. 1 (1963), 139-148. https://doi.org/10.1007/BF02759700
  16. J. Stampfli, Which weighted shifts are subnormal?, Pacific J. Math. 17 (1966), 367-379. https://doi.org/10.2140/pjm.1966.17.367

Cited by

  1. Absolutely norm attaining paranormal operators vol.465, pp.1, 2012, https://doi.org/10.1016/j.jmaa.2018.05.024
  2. A NOTE ON POSITIVE OPERATORS vol.100, pp.1, 2012, https://doi.org/10.1017/s0004972718001296