23 October 2012

17:00

to

18:23

Vladimir Muller

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 the well-known fact for $n = 1$ that the numerical radius $w(T)$ of a
single operator T satisfies $w(T)\ge \|T\|/2$.