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

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Published: Mar 30, 2015
Keywords:
subnormal, k-hyponormal, weakly subnormal
Mathematics Subject Classification:
Primary 47B20, 47B37, 47A13, 28A50, Secondary 44A60, 47-04, 47A20

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Jun Ik Lee
Department of Mathematics Education Sangmyung University Seoul 110-743, Republic of Korea

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.


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Supporting Agencies

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

References

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