An Algorithm for Quartically Hyponormal Weighted Shifts

- Journal title : Kyungpook mathematical journal
- Volume 51, Issue 2, 2011, pp.187-194
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2011.51.2.187

Title & Authors

An Algorithm for Quartically Hyponormal Weighted Shifts

Baek, Seung-Hwan; Jung, Il-Bong; Moo, Gyung-Young;

Baek, Seung-Hwan; Jung, Il-Bong; Moo, Gyung-Young;

Abstract

Examples of a quartically hyponormal weighted shift which is not 3-hyponormal are discussed in this note. In [7] Exner-Jung-Park proved that if (x) : with 0 < x , then is quartically hyponormal but not 4-hyponormal. And, Curto-Lee([5]) improved their result such as that if : with 0 < x , then is quartically hyponormal but not 3-hyponormal. In this note, we improve slightly Curto-Lee`s extremal value by using an algorithm and computer software tool.

Keywords

quartically hyponormal operators;cubically hyponormal operators;quadratically hyponormal operators;weighted shifts;

Language

English

Cited by

References

1.

R. Curto, Quadratically hyponormal weighted shifts, Integral Equations Operator Theory, 13(1990), 49-66.

2.

R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Integral Equations Operator Theory, 17(1993), 202-246.

3.

R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, II, Integral Equations Operator Theory, 17(1993), 202-246.

4.

R. Curto and I. B. Jung, Quadratically hyponormal weighted shifts with two equal weights, Integral Equations Operator Theory, 37(2000), 208-231.

5.

R. Curto and S. H. Lee, Quartically hyponormal weighted shifts need not be 3- hyponormal, J. Math. Anal. Appl., 314(2006), 455-463.

6.

R. Curto and M. Putinar, Nearly subnormal operators and moment problems, J. Funct. Anal., 115(1993), 480-497.

7.

G. Exner, I. B. Jung, and S. S. Park, Weakly n-hyponormal weighted shifts and their examples, Integral Equations Operator Theory, 54(2006), 215-233.

8.

I. B. Jung and S. S. Park, Quadratically hyponormal weighted shifts and their exam- ples, Integral Equations Operator Theory, 36(2000), 480-498.

9.

I. B. Jung and S. S. Park, Cubically hyponormal weighted shifts and their examples, J. Math. Anal. Appl., 247(2000), 557-569.

10.

Wolfram Research, Inc., Mathematica, Version 8.0, Wolfram Research Inc., Cham- paign, IL, 2010.