Blaschke products and the Crouzeix conjecture
Speaker:
Pamela Gorkin, Bucknell University
Date and Time:
Friday, October 29, 2021 - 11:00am to 11:50am
Location:
Online
Abstract:
Let A be a n×n matrix and p a complex polynomial. Let W(A) denote the numerical range (or field of values) of a matrix; that is, W(A)={⟨Ax,x⟩:x∈Cn,‖x‖=1}. M. Crouzeix conjectured that for every polynomial p we have
‖p(A)‖≤2supz∈W(A)|p(z)|. In this talk, we give some background on the conjecture, and explain why we consider it in the model space setting. We then turn to Blaschke products, with a focus on properties that we hope will aid our understanding of the conjecture.