A von Neumann type inequality for an annulus

Abstract

Let Ar = {r < |z| < 1} be an annulus. We consider the class of operatorsand show that for every bounded holomorphic function φ on Ar : supwhere the constant √ 2 is the best possible. We do this by characterizing the calcular norm induced on H ∞ (Ar) by Fr as the multiplier norm of a suitable holomorphic function space on Ar.