Open AccessSCHWARZ'S LEMMA IN NORMED LINEAR SPACES
Author(s) -
Lawrence A. Harris
Publication year - 1969
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.62.4.1014
Subject(s) - mathematics , surjective function , isometry (riemannian geometry) , unit sphere , open mapping theorem (functional analysis) , banach space , hilbert space , holomorphic function , operator theory , pure mathematics , linear map , operator norm , lp space , banach manifold
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.