SCHWARZ'S LEMMA IN NORMED LINEAR SPACES
- 1 April 1969
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 62 (4) , 1014-1017
- https://doi.org/10.1073/pnas.62.4.1014
Abstract
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.Keywords
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