Differentiable semigroups are Lie groups
We present here a modern, detailed proof to the following theorem which was introduced by Garrett Birkhoff [1] in 1938. If S is a local semigroup with neighborhood of 1 homeomorphic to a Banach space and with multiplication strongly differentiable at 1, then S is a local Lie Group. Although this the...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000652 |
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| Summary: | We present here a modern, detailed proof to the following theorem which was introduced
by Garrett Birkhoff [1] in 1938. If S is a local semigroup with neighborhood of 1 homeomorphic to a
Banach space and with multiplication strongly differentiable at 1, then S is a local Lie Group. Although
this theorem is more than 50 years old and remains the strongest result relating to Hilbert's fifth problem
in the infinite dimensional setting, it is frequently overlooked in favor of weaker results. Therefore, it
is the goal of the authors here to clarify its importance and to demonstrate a proofwhich is more accessible
to contemporary readers than the one offered by Birkhoff. |
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| ISSN: | 0161-1712 1687-0425 |