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Autumn 2016 Norm inequalities for elementary operators related to contractions and operators with spectra contained in the unit disk in norm ideals
Stefan Milošević
Adv. Oper. Theory 1(2): 147-159 (Autumn 2016). DOI: 10.22034/aot.1609.1019

Abstract

If $A,B \in \mathcal {B}(\mathcal {H})$ are normal contractions, then for every $X \in \mathcal {C}_{||| \cdot |||}(\mathcal {H})$ and $\alpha > 0$ holds $$\Big|\Big|\Big| (I - A^{*}A)^{\frac{\alpha}{2}} X(I - B^{*}B)^{\frac{\alpha}{2}} \Big|\Big|\Big| \leqslant \Big|\Big|\Big| \sum_{n=0}^\infty (-1)^{n} \binom{\alpha}{n}A^{n} X B^{n} \Big|\Big|\Big|,$$ which generalizes a result of D.R. Jocić [Proc. Amer. Math. Soc. 126 (1998), no. 9, 2705-2713] for $\alpha$ not being an integer. Similar inequalities in the Schatten $p$-norms, for non-normal $A,B$ and in the $Q$-norms if one of $A$ or $B$ is normal, are also given.

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Stefan Milošević. "Norm inequalities for elementary operators related to contractions and operators with spectra contained in the unit disk in norm ideals." Adv. Oper. Theory 1 (2) 147 - 159, Autumn 2016. https://doi.org/10.22034/aot.1609.1019

Information

Received: 29 September 2016; Accepted: 1 December 2016; Published: Autumn 2016
First available in Project Euclid: 4 December 2017

zbMATH: 1355.47006
MathSciNet: MR3723616
Digital Object Identifier: 10.22034/aot.1609.1019

Subjects:
Primary: 47B47
Secondary: 47A30 , 47A63 , 47B10 , 47B15 , 47B49

Keywords: $Q$-norm , elementary operator , norm inequality

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.1 • No. 2 • Autumn 2016
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