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

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