Differentiable projections and differentiable semigroups
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- by J. P. Holmes PDF
- Proc. Amer. Math. Soc. 41 (1973), 251-254 Request permission
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.References
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- John P. Holmes, Differentiable power-associative groupoids, Pacific J. Math. 41 (1972), 391–394. MR 305104
- Sam B. Nadler Jr., A characterization of the differentiable submanifolds of $R^{n}$, Proc. Amer. Math. Soc. 17 (1966), 1350–1352. MR 203737, DOI 10.1090/S0002-9939-1966-0203737-2
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 251-254
- MSC: Primary 58C25
- DOI: https://doi.org/10.1090/S0002-9939-1973-0375378-1
- MathSciNet review: 0375378