"Von Neumann Inequalities with Respect to Dirichlet Spaces"

By

**Hakkı Turgay Kaptanoğlu**

Abstract: If
$T$ is a contraction on a Hilbert space $H$ and $p$ is a complex polynomial,
von Neumann inequality states that the norm of $p(T)$ is at most the maximum of
$p$ on the unit disc. Dirichlet spaces $D_q$ are reproducing kernel Hilbert spaces of holomorphic functions in the unit ball of $C^N$ with
kernels $K_q(z,w)=(1-\langle z,w\rangle)^{-(1+N+q)}$
for $q>-(1+N)$. Drury and Arveson extended von
Neumann inequality to an $N$-tuple of

contractions on $H$ using the multiplier norm of $p$ on $D_{-N}$.
We discuss von Neumann inequalities for an $N$-tuple
of contractions on $H$ with respect to general $D_q$.

Tea and cookies will be served before the
seminar.

**Date: ****Thursday, March 18, 2010**

**Time: ****14.40**

**Place: ****Mathematics Seminar Room,
SA-141**