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Journal List > Proc Natl Acad Sci U S A > v.62(4); Apr 1969

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Proc Natl Acad Sci U S A. 1969 April; 62(4): 1014–1017.
PMCID: PMC223606
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SCHWARZ'S LEMMA IN NORMED LINEAR SPACES*
Lawrence A. Harris†
DEPARTMENT OF MATHEMATICS, CORNELL UNIVERSITY
† Present address: Department of Mathematics, Harvard University.
* Thesis research supported by the NSF Graduate Fellowship program.
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.
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