Abstract

We set up an abstract framework that allows the investigation of Iwasawa decompositions for involutive infinite-dimensional Lie groups modeled on Banach spaces. This provides a method to 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 $1<p<\infty$.

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