Annals of Functional Analysis

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

Junxiang Cheng and Jiangtao Yuan

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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

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

First available in Project Euclid: 12 May 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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