Korean J. Math.  Vol 23, No 1 (2015)  pp.199-203
DOI: https://doi.org/10.11568/kjm.2015.23.1.199

Weakly subnormal weighted shifts need not be 2-hyponormal

Jun Ik Lee


In this paper we give an example which is a weakly subnormal weighted shift but not 2-hyponormal. Also, we show that every partially normal extension of an isometry $T$ needs not be 2-hyponormal even though $\text{p.n.e.}(T)$ is weakly subnormal.


subnormal, k-hyponormal, weakly subnormal

Subject classification

Primary 47B20, 47B37, 47A13, 28A50; Secondary 44A60, 47-04, 47A20


This research was Supported by a 2014 Research Grant from SangMyung University.

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J. Bram, Subnormal operators, Duke Math. J. 22 (1955), 75–94. (Google Scholar)

R.E. Curto, Quadratically hyponormal weighted shifts, Integral Equations Operator Theory 13 (1990), 49–66. (Google Scholar)

R.E. Curto, I.B. Jung and S. S. Park, A characterization of k-hyponormality via weak subnormality, J. Math. Anal. Appl. 279 (2003), 556–568. (Google Scholar)

R.E. Curto and W.Y. Lee, Towards a model theory for 2-hyponormal operators, Integral Equations Operator Theory 44 (2002), 290–315. (Google Scholar)

J. Conway, The Theory of Subnormal Operators, Mathematical Surveys and Monographs, vol. 36, Amer. Math. Soc., Providence, 1991. (Google Scholar)

R. Curto, S.H. Lee and W.Y. Lee, A new criterion for k-hyponormality via weak subnormality, Proc. Amer. Math. Soc. (to appear) (Google Scholar)

R. Curto, P. Muhly and J. Xia, Hyponormal pairs of commuting operators, Operator Theory: Adv. Appl. 35 (1988), 1–22. (Google Scholar)


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