Let A be a complex Banach algebra with unit. It was shown by Williams that elements a, b ∈ A commute if and only if supλ∈C ||exp(λb) a exp(-λb)||< ∞. This result allows us to obtain an analog of the von Neumann-Fuglede-Putnam theorem in case of normal elements in a complex Banach algebra. An abstract version of Picard theorem is obtained in this context.
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