Analytic Mappings Between LB-spaces and Applications in Infinite-Dimensional Lie Theory

2008/07/23 by Rafael Dahmen, Dahmen, Rafael
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #math.FA #math.GR

paper · pdf · doi:10.48550/arxiv.0807.3655

arxiv created 2008/07/28 · arxiv updated 2009/12/01

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: (a) groups of germs of analytic diffeomorphisms around a compact set in a Banach space and (b) unions of ascending sequences of Banach Lie groups.

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