An abstract approach to the Crouzeix conjecture

Raphaël Clouâtre, Maëva Ostermann, Thomas Ransford

Let $A$ be a uniform algebra, $\theta :A\to M_n(\mathbb{C})$ be a continuous homomorphism and $\alpha :A\to A$ be an antilinear contraction such that \[ \|θ(f)+θ(α(f))^*\|\le 2\|f\| \quad(f\in…