Continuous homomorphisms are differentiable
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- by J. P. Holmes PDF
- Proc. Amer. Math. Soc. 65 (1977), 277-281 Request permission
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 $[0,1]$.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 277-281
- MSC: Primary 58C25; Secondary 46H99
- DOI: https://doi.org/10.1090/S0002-9939-1977-0455016-3
- MathSciNet review: 0455016