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http://dx.doi.org/10.14403/jcms.2018.31.1.325

THE MODULUS MULTIPLICATION TRANSFORM OF BOUNDED LINEAR OPERATORS  

Lee, Jun Ik (Department of Mathematics Education Sangmyung University)
Lee, Sang Hoon (Department of Mathematics Chungnam National University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.31, no.3, 2018 , pp. 325-331 More about this Journal
Abstract
In this paper, we study which transform preserves the k-hyponormality of weighted shifts. For this, we introduce a new transform, the modulus multiplication transform, and then examine various properties of it.
Keywords
Aluthge transform; modulus multiplication transform; subnormal; k-hyponormal; weighted shifts;
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1 R. Curto, Y. Poon, and J. Yoon, Subnormality of Bergman-like weighted shifts, J. Math. Anal. Appl. 308 (2005), 334-342.   DOI
2 K. Dykema and H. Schultz, Brown measure and iterates of the Aluthge transform for some operators arising from measurable actions, Trans. Amer. Math. Soc. 361 (2009), 6583-6593.   DOI
3 G. R. Exner, Aluthge transforms and $n$n-contractivity of weighted shifts, J. Operator Theory, 61 (2009), no. 2, 419-438.
4 C. Foias, I. Jung, E. Ko, and C. Pearcy, Complete contractivity of maps associated with the Aluthge and Duggal transformations, Pacific J. Math. 209 (2003), 249-359.   DOI
5 S. H. Lee, W. Y. Lee, and J. Yoon, Subnormality of Aluthge transform of weighted shifts, Integral Equations Operator Theory, 72 (2012), 241-251.   DOI
6 S. H. Lee, W. Y. Lee, and J. Yoon, The mean transform of bounded linear operators, J. Math. Anal. Appl. 410 (2014), 70-81.   DOI
7 V. Paulsen, Completely bounded maps and dilations, Pitmam Research Notes in Mathematics Series, vol. 146, Longman Sci. Tech. New York, 1986.
8 T. Yamazaki, An expression of spectral radius via Aluthge transformation, Proc. Amer. Math. Soc. 130 (2002), 1131-1137.   DOI
9 T. Yoshino, The p-Hyponormality of the Aluthge transformation, Interdiscip. Inform. Sci. 3 (1997), 91-93.
10 A. Aluthge, On p-hyponormal Operators for 0 < p < 1, Integral Equations Operator Theory, 13 (1990), 307-315.   DOI
11 M. Cho, I. B. Jung, and W. Y. Lee, On Aluthge Transforms of p-hyponormal Operators, Integral Equations Operator Theory, 53 (2005), 321-329.   DOI
12 J. Conway, The Theory of Subnormal Operators, Mathematical Surveys and Monographs, vol. 36, Amer. Math. Soc. Providence, 1991.
13 R. Curto, P. Muhly, and J. Xia, Hyponormal pairs of commuting operators, Operator Theory: Adv. Appl. 35 (1988), 1-22.
14 R. Curto and S. Park, k-hyponormality of powers of weighted shifts, Proc. Amer. Math. Soc. 131 (2003), 2761-2769.   DOI