Proceedings of the American Mathematical Society

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



Differentiable projections and differentiable semigroups

Author: J. P. Holmes
Journal: Proc. Amer. Math. Soc. 41 (1973), 251-254
MSC: Primary 58C25
MathSciNet review: 0375378
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Abstract: Suppose $ X$ is a Banach space, $ G$ is a connected open subset of $ X$, and $ p$ is a continuously Fréchet differentiable function from $ G$ into $ G$ satisfying $ p(p(x)) = p(x)$ for each $ x$ in $ G$. We prove that $ p(G)$ is a differentiable submanifold of $ X$ and use this result to show that the maximal subgroup containing an idempotent in a differentiable semigroup is a Lie group.

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Keywords: Differentiable manifold, differentiable semigroup
Article copyright: © Copyright 1973 American Mathematical Society