M. I. Karahanyan

On the abstract theorem of Picard

(Lobachevskii Journal of Mathematics, Vol.18, pp.127-130 )

Let A be a complex Banach algebra with unit. It was shown by Williams that elements a, bA 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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