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Journal of Lie Theory 34 (2024), No. 1, 207--236
Copyright Heldermann Verlag 2024

A Category of Banach Space Functors

Mauricio Garay
Institut Fibonacci, Bures-sur-Yvette, France

Duco van Straten
Institut für Mathematik, Johannes-Gutenberg-Universität, Mainz, Germany

We introduce a sheaf theoretic viewpoint on functional analysis designed for infinite dimensional Lie group actions. We develop functional calculus for Banach space valued functors and, in particular, prove the existence of an exponential map for a certain class of operators that generalise first order partial differential operators. These results can be used for proving normal forms and versal deformations theorems in KAM theory.

Keywords: Infinite dimensional Lie groups, dynamical systems, KAM theory, normal forms, versal deformations.

MSC: 37J40.

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