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On joint numerical radius


Author: Vladimir Müller
Journal: Proc. Amer. Math. Soc. 142 (2014), 1371-1380
MSC (2010): Primary 47A12; Secondary 47A13
DOI: https://doi.org/10.1090/S0002-9939-2014-11876-4
Published electronically: January 29, 2014
MathSciNet review: 3162257
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Abstract: Let $ T_1,\dots ,T_n$ be bounded linear operators on a complex Hilbert space $ H$. We study the question whether it is possible to find a unit vector $ x\in H$ such that $ \vert\langle T_jx,x\rangle \vert$ is large for all $ j$. Thus we are looking for a generalization of a well-known fact for $ n=1$ that the numerical radius $ w(T)$ of a single operator $ T$ satisfies $ w(T)\ge \Vert T\Vert/2$.


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Additional Information

Vladimir Müller
Affiliation: Mathematical Institute, Czech Academy of Sciences, Zitna 25, 115 67 Praha 1, Czech Republic
Email: muller@math.cas.cz

DOI: https://doi.org/10.1090/S0002-9939-2014-11876-4
Keywords: Joint numerical range, numerical radius
Received by editor(s): November 16, 2011
Received by editor(s) in revised form: May 23, 2012
Published electronically: January 29, 2014
Additional Notes: This research was supported by grants 201/09/0473 of GA ČR, IAA100190903 of GA AV ČR and RVO: 67985840
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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