"Von Neumann Inequalities with Respect to Dirichlet Spaces"




Hakkı Turgay Kaptanoğlu



AbstractIf $T$ 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