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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
DOI: https://doi.org/10.1090/S0002-9939-1973-0375378-1
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.


References [Enhancements On Off] (What's this?)

  • [1] G. Birkhoff, Analytical groups, Trans. Amer. Math. Soc. 43 (1938), 61-101. MR 1501934
  • [2] J. Dieudonné, Fondements de l'analyse moderne, Pure and Appl. Math., vol. 10, Academic Press, New York and London, 1960. MR 22 #11074.
  • [3] J. P. Holmes, Differentiable power associative groupoids, Pacific J. Math. 41 (1972), 319-394. MR 0305104 (46:4234)
  • [4] S. B. Nadler, Jr., A characterization of the differentiable submanifolds of $ {R^n}$, Proc. Amer. Math. Soc. 17 (1966), 1350-1352. MR 34 #3586. MR 0203737 (34:3586)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0375378-1
Keywords: Differentiable manifold, differentiable semigroup
Article copyright: © Copyright 1973 American Mathematical Society

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