### Seminar talk by Hartz: How can you compute the multiplier norm?

Happy new year!

Next Thursday, January 7th, 2021, Michael Hartz will speak in our Operator Algebras and Operator Theory seminar.

Title: How can you compute the multiplier norm?

Time: 15:30-16:30

Multipliers of reproducing kernel Hilbert spaces arise in various contexts in operator theory and complex analysis. A basic example is the Hardy space $H^2$, whose multiplier algebra is $H^\infty$, the algebra of bounded holomorphic functions. In particular, the norm of a multiplier on $H^2$ is the pointwise supremum norm.
For general reproducing kernel Hilbert spaces, the multiplier norm can be computed by testing positivity of $n \times n$ matrices analogous to the classical Pick matrix. For $H^2$, $n=1$ suffices. I will talk about when it suffices to consider matrices of bounded size $n$. Moreover, I will explain how this problem is related to subhomogeneity of operator algebras.