On joint numerical radius

Müller, Vladimir

doi:10.1090/S0002-9939-2014-11876-4

On joint numerical radius
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by Vladimir Müller

Proc. Amer. Math. Soc. 142 (2014), 1371-1380

DOI: https://doi.org/10.1090/S0002-9939-2014-11876-4

Published electronically: January 29, 2014

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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 $|\langle T_jx,x\rangle |$ 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 $w(T)\ge \|T\|/2$.

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