Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 9, Number 4 (2018), 463-473.
A note on the -numerical radius and the -Aluthge transform in finite factors
We prove that for any two elements , in a factor , if commutes with all the unitary conjugates of , then either or is in . Then we obtain an equivalent condition for the situation that the -numerical radius is a weakly unitarily invariant norm on finite factors, and we also prove some inequalities on the -numerical radius on finite factors. As an application, we show that for an invertible operator in a finite factor , is in the weak operator closure of the set , where is a polynomial, is the -Aluthge transform of , and .
Ann. Funct. Anal., Volume 9, Number 4 (2018), 463-473.
Received: 5 August 2017
Accepted: 16 October 2017
First available in Project Euclid: 23 April 2018
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Zhou, Xiaoyan; Fang, Junsheng; Wen, Shilin. A note on the $C$ -numerical radius and the $\lambda$ -Aluthge transform in finite factors. Ann. Funct. Anal. 9 (2018), no. 4, 463--473. doi:10.1215/20088752-2017-0061. https://projecteuclid.org/euclid.afa/1524470416