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Schmoeger has shown that if Weyl's theorem holds for an isoloid Banach space operator T ∈ B(X) with stable index, then it holds for f (T ) whenever f ∈ Holo σ(T ) is a function holomorphic on some neighbourhood of the spectrum of T . In this note we establish a converse.doi:10.17398/2605-5622.214.171.124 fatcat:iigsgqbt4bgono3xdcc67msa6i