Analytic mappings between LB-spaces and applications in infinite-dimensional Lie theory |
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Authors: | Rafael Dahmen |
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Affiliation: | 1. Institut für Mathematik, Universit?t Paderborn, Warburger Str. 100, 33098, Paderborn, Germany
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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 ${bigcup_{ninmathbb {N}}G_n}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 èn ? mathbb NGn{bigcup_{ninmathbb {N}}G_n} where the G n are Banach Lie groups. |
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