Abstract view
Lie Groups of Measurable Mappings


Published:20031001
Printed: Oct 2003
Abstract
We describe new construction principles for infinitedimensional Lie
groups. In particular, given any measure space $(X,\Sigma,\mu)$ and
(possibly infinitedimensional) Lie group $G$, we construct a Lie
group $L^\infty (X,G)$, which is a Fr\'echetLie group if $G$ is so.
We also show that the weak direct product $\prod^*_{i\in I} G_i$ of an
arbitrary family $(G_i)_{i\in I}$ of Lie groups can be made a Lie
group, modelled on the locally convex direct sum $\bigoplus_{i\in I}
L(G_i)$.
MSC Classifications: 
22E65, 46E40, 46E30, 22E67, 46T20, 46T25 show english descriptions
Infinitedimensional Lie groups and their Lie algebras: general properties [See also 17B65, 58B25, 58H05] Spaces of vector and operatorvalued functions Spaces of measurable functions ($L^p$spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Loop groups and related constructions, grouptheoretic treatment [See also 58D05] Continuous and differentiable maps [See also 46G05] Holomorphic maps [See also 46G20]
22E65  Infinitedimensional Lie groups and their Lie algebras: general properties [See also 17B65, 58B25, 58H05] 46E40  Spaces of vector and operatorvalued functions 46E30  Spaces of measurable functions ($L^p$spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 22E67  Loop groups and related constructions, grouptheoretic treatment [See also 58D05] 46T20  Continuous and differentiable maps [See also 46G05] 46T25  Holomorphic maps [See also 46G20]
