Iwasawa decompositions of some infinite-dimensional Lie groups

Abstract

We set up an abstract framework that allows the investigation of Iwasawa decompositions for involutive infinite-dimensional Lie groups modeled on Banach spaces. As an application, we construct Iwasawa decompositions for classical real or complex Banach-Lie groups associated with the Schatten ideals ${\mathfrak{S}}_p(\mathcal{H})$ on a complex separable Hilbert space $\mathcal{H}$ if $1<p<\infty$.

25 pages