Seminario di analisi matematica
ore
16:00
The classical von Neumann inequality shows that for any contraction T on
a Hilbert space, the operator norm of $p(T)$ satisfies
\[ \|p(T)\| \le \sup_{|z| \le 1} |p(z)|. \]
Whereas Ando extended this inequality to pairs of commuting
contractions, the corresponding statement for triples of commuting
contractions is false. However, it is still not known whether von
Neumann's inequality for triples of commuting contractions holds up to a
constant. I will talk about this question and about function theoretic
upper bounds for $\|p(T)\|$.