Weakly subnormal weighted shifts need not be 2-hyponormal

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doi:http://dx.doi.org/10.11568/kjm.2015.23.1.199

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Weakly subnormal weighted shifts need not be 2-hyponormal

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subnormal k-hyponormal weakly subnormal

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초록

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.

Abstract

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.

참고문헌 (7)

J. Bram, "Subnormal operators", Duke Math. J, 22, pp.75~94 (1955)
R.E. Curto, "Quadratically hyponormal weighted shifts", Integral Equations Oper-ator Theory, 13, pp.49~66 (1990)
R.E. Curto, "A characterization of k-hyponormality via weak subnormality", J. Math. Anal. Appl, 279, pp.556~568 (2003)
R.E. Curto, "Towards a model theory for 2-hyponormal operators", Integral Equations Operator Theory, 44, pp.290~315 (2002)
J. Conway, "Amer. Math. Soc." (1991), Providence
R. Curto, "A new criterion for k-hyponormality via weak subnormality", Proc. Amer. Math. Soc
R. Curto, "Hyponormal pairs of commuting operators", Op-erator Theory: Adv. Appl, 35, pp.1~22 (1988)

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