  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 $1<p<\infty$.
