Abstract
We give a sufficient criterion for complex analyticity of nonlinear maps defined on direct limits of normed spaces. This tool is then used to construct new classes of (real and complex) infinite dimensional Lie groups: The group DiffGerm(K, X) of germs of analytic diffeomorphisms around a compact set K in a Banach space X and the group S n∈N Gn where the Gn are Banach Lie groups.
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