Annals of Functional Analysis

Aluthge Transforms of $(\mathcal{C}_{p},\alpha)$-Hyponormal Operators

Junxiang Cheng and Jiangtao Yuan

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Abstract

Recently, the class of $(\mathcal{C}_{p},\alpha)$-hyponormal operators is introduced and the Aluthge transforms of such operators is discussed by some researchers. This paper is to give a further development of the Aluthge transforms of $(\mathcal{C}_{p},\alpha)$-hyponormal operators by using Loewner-Heinz inequality, Furuta inequality and Lauric's lemma. Especially, it is shown that, if $p\ge 1$, $\alpha\ge 1/2$ and $T$ is $(\mathcal{C}_{p},\alpha)$-hyponormal, then the Aluthge transform $T(1/2,1/2)$ is $(\mathcal{C}_{4p\alpha/\beta},\beta)-hyponormal$ where $0 \lt \beta \le 1$ and $T(1/2,1/2)=|T|^{1/2}U|T|^{1/2}$.

Article information

Source
Ann. Funct. Anal., Volume 2, Number 1 (2011), 100-104.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1399900265

Digital Object Identifier
doi:10.15352/afa/1399900265

Mathematical Reviews number (MathSciNet)
MR2811210

Zentralblatt MATH identifier
1230.47042

Subjects
Primary: 47B20: Subnormal operators, hyponormal operators, etc.
Secondary: 47A63: Operator inequalities

Keywords
Loewner-Heinz inequality Furuta inequality ‎hyponormal operator ‎Aluthge transform Schatten $p$-class

Citation

Cheng, Junxiang; Yuan, Jiangtao. Aluthge Transforms of $(\mathcal{C}_{p},\alpha)$-Hyponormal Operators. Ann. Funct. Anal. 2 (2011), no. 1, 100--104. doi:10.15352/afa/1399900265. https://projecteuclid.org/euclid.afa/1399900265


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