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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Continuous homomorphisms are differentiable


Author: J. P. Holmes
Journal: Proc. Amer. Math. Soc. 65 (1977), 277-281
MSC: Primary 58C25; Secondary 46H99
MathSciNet review: 0455016
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Abstract: Suppose X is a Banach space, D is an open set of X containing 0, and V is a continuously differentiable function from DXD to X satisfying $ V(0,x) = V(x,0) = x$ for each x in D. If T is a continuous function from $ [0,1]$ into D satisfying $ T(0) = 0$ and $ V(T(s),T(t)) = T(s + t)$ whenever each of s, t, and $ s + t$ is in $ [0,1]$ then T is continuously differentiable on $ [0,1]$.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0455016-3
Keywords: Differentiable homomorphism, automatic differentiability, one parameter semigroups
Article copyright: © Copyright 1977 American Mathematical Society