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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0296208-1
PII: S 0002-9939(1972)0296208-1
Keywords: Topological semigroup, differentiable, manifold
Article copyright: © Copyright 1972 American Mathematical Society