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Differentiable semigroups with a neighborhood of the identity homeomorphic to a Banach space

Author: J. W. Neuberger
Journal: Proc. Amer. Math. Soc. 34 (1972), 595-600
MSC: Primary 22A20
MathSciNet review: 0296208
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Abstract: Suppose S is a topological semigroup with identity e, H is a Banach space and there is a homeomorphism g from an open subset of S containing e onto H. Theorem. Suppose that $ V(x,y) = g({g^{ - 1}}(x){g^{ - 1}}(y))$ for all x, y in H for which the second expression is defined. If V is $ {C^{(2)}}$ then there is an open subset D of S containing e so that if q is in D, then for some number t and some one-parameter subgroup f of S, $ q = f(t)$.

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  • [1] Garrett Birkhoff, Analytical groups, Trans. Amer. Math. Soc. 43 (1938), 61-101. MR 1501934
  • [2] J. Dieudonné, Foundations of modern analysis, Pure and Appl. Math., vol. 10, Academic Press, New York, 1960. MR 22 #11074. MR 0120319 (22:11074)
  • [3] B. Maissen, Lie-Gruppen mit Banachräume als Parameterräume, Acta Math. 108 (1962), 229-270. MR 26 #262. MR 0142693 (26:262)
  • [4] P. S. Mostert and A. L. Shields, Semigroups with identity on a manifold, Trans. Amer. Math. Soc. 91 (1959), 380-389. MR 21 #4204. MR 0105463 (21:4204)
  • [5] J. W. Neuberger, Continuous products and nonlinear integral equations, Pacific J. Math. 8 (1958), 529-549. MR 21 #1509. MR 0102723 (21:1509)
  • [6] J. von Neumann, Über die analytischen Eigenschaften von Gruppen linearer Transformationen und ihrer Darstellungen, Math. Z. 30 (1929), 3-42. MR 1545040
  • [7] F. Nevanlinna and R. Nevanlinna, Absolute analysis, Die Grundlehren der math. Wissenschaften, in Einzeldarstellungen mit besonderer Beruchsichtigung der Anwendungsgebiete, Band 102, Springer-Verlag, Berlin, 1959. MR 22 #12176. MR 0121438 (22:12176)

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Keywords: Topological semigroup, differentiable, manifold
Article copyright: © Copyright 1972 American Mathematical Society

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