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Let $\mathfrak{g}$ be a basic simple Lie superalgebra over an algebraicallyclosed field of characteristic zero, and $\theta$ an involution of$\mathfrak{g}$ preserving a nondegenerate invariant form. We prove that either$\theta$ or $\delta\circ\theta$ admits an Iwasawa decomposition, where $\delta$is the canonical grading automorphism $\delta(x)=(-1)^{\overline{x}}x$. Theproof uses the notion of generalized root systems as developed by Serganova,and follows from a more general result on centralizers of certain tori comingfrom semisimple automorphisms of the Lie superalgebra $\mathfrak{g}$.

Iwasawa Decomposition for Lie Superalgebras