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

by Orr Shalit

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

Zoom link: Email me.

Abstract:

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.

This is joint work with Alexandru Aleman, John McCarthy and Stefan Richter