# On the Iterated Duggal Transforms

Cho, Muneo;Jung, Il-Bong;Lee, Woo-Young

• Accepted : 2009.08.21
• Published : 2009.12.31
• 22 4

#### Abstract

For a bounded operator T = $U{\mid}T{\mid}$ (polar decomposition), we consider a transform b $\widehat{T}$ = ${\mid}T{\mid}U$ and discuss the convergence of iterated transform of $\widehat{T}$ under the strong operator topology. We prove that such iteration of quasiaffine hyponormal operator converges to a normal operator under the strong operator topology.

#### Keywords

Aluthge transform;hyponormal operator;quasiaffinity

#### References

1. A. Aluthge, On p-hyponormal operators for 0 < p < 1, Integral Equations Operator Theory, 13(1990), 307-315. https://doi.org/10.1007/BF01199886
2. T. Ando and T. Yamazaki, The iterated Aluthge transforms of a 2-by-2 matrix converge, Linear Algebra Appl., 375(2003), 299-309. https://doi.org/10.1016/j.laa.2003.06.002
3. J. Antezana, E. Pujals, and D. Stojanoff, Convergence of the iterated Aluthge transform sequence for diagonalizable matrices, Advances Math., 216(2007), 255-278. https://doi.org/10.1016/j.aim.2007.05.009
4. M. Cho, I. Jung, and W. Lee, On Aluthge transforms of p-hyponormal operators, Integral Equations Operator Theory, 53(2005), 321-329. https://doi.org/10.1007/s00020-003-1324-y
5. C. Foias, I. Jung, E. Ko, and C. Pearcy, Complete contractivity of maps associated with the Aluthge and Duggal transforms, Pacific J. Math., 209(2003), 249-359. https://doi.org/10.2140/pjm.2003.209.249
6. P. R. Halmos, A Hilbert space problem book, 2nd ed., New York, 1982.
7. I. S. Hwang and W. Y. Lee, The spectrum is continuous on the set of p-hyponormal operators, Math. Z., 235(2000), 151-157. https://doi.org/10.1007/s002090000128
8. I. Jung, E. Ko, and C. Pearcy, Aluthge transforms of operators, Integral Equations Operator Theory, 37(2000), 437-448. https://doi.org/10.1007/BF01192831
9. I. Jung, E. Ko, and C. Pearcy, The iterated Aluthge transform of an operator, Integral Equations Operator Theory, 45(2003), 375-387. https://doi.org/10.1007/s000200300012

#### Cited by

1. Subscalarity of operator transforms vol.288, pp.17-18, 2015, https://doi.org/10.1002/mana.201500037