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November 2018 A note on the C-numerical radius and the λ-Aluthge transform in finite factors
Xiaoyan Zhou, Junsheng Fang, Shilin Wen
Ann. Funct. Anal. 9(4): 463-473 (November 2018). DOI: 10.1215/20088752-2017-0061

Abstract

We prove that for any two elements A, B in a factor M, if B commutes with all the unitary conjugates of A, then either A or B is in CI. Then we obtain an equivalent condition for the situation that the C-numerical radius ωC() is a weakly unitarily invariant norm on finite factors, and we also prove some inequalities on the C-numerical radius on finite factors. As an application, we show that for an invertible operator T in a finite factor M, f(λ(T)) is in the weak operator closure of the set {i=1nziUif(T)UinN,(Ui)1inU(M),i=1n|zi|1}, where f is a polynomial, λ(T) is the λ-Aluthge transform of T, and 0λ1.

Citation

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Xiaoyan Zhou. Junsheng Fang. Shilin Wen. "A note on the C-numerical radius and the λ-Aluthge transform in finite factors." Ann. Funct. Anal. 9 (4) 463 - 473, November 2018. https://doi.org/10.1215/20088752-2017-0061

Information

Received: 5 August 2017; Accepted: 16 October 2017; Published: November 2018
First available in Project Euclid: 23 April 2018

zbMATH: 07002084
MathSciNet: MR3871907
Digital Object Identifier: 10.1215/20088752-2017-0061

Subjects:
Primary: 47A12
Secondary: 46L10

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 4 • November 2018
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