Schwarz'S lemma in normed linear spaces.
نویسنده
چکیده
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.
منابع مشابه
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Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/fun/notes 2016-17/02 banach.pdf] 1. Basic definitions 2. Riesz’ Lemma 3. Counter-examples for unique norm-minimizing element 4. Normed spaces of continuous linear maps 5. Dual spaces of normed spaces 6. Banach-Steinhaus/uniform-boundedness theorem 7. Open mapping theorem 8. C...
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ورودعنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 62 4 شماره
صفحات -
تاریخ انتشار 1969