Abstract
Let Ar={r<|z|<1} be an annulus. We consider the class of operatorsFr:={T∈B(H):r2T−1(T−1)⁎+TT⁎≤r2+1,σ(T)⊂Ar} and show that for every bounded holomorphic function ϕ on Ar:supT∈Fr||ϕ(T)||≤2||ϕ||∞, where 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.
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