SCHWARZ'S LEMMA IN NORMED LINEAR SPACES*

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RESUMO

In this paper we show that any Fréchet holomorphic function mapping the open unit ball of one normed linear space into the closed unit ball of another must be a linear mapping if the Fréchet derivative of the function at zero is a surjective isometry. From this fact we deduce a Banach-Stone theorem for operator algebras which generalizes that of R. V. Kadison.

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