Geodesic
Stein Extensions of Riemann Symmetric Spaces and some Generalization
Journal of Lie theory, Tome 13 (2003) no. 2, pp. 565-572.

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We give a proof that the Akhiezer-Gindikin domain D is contained in the "Iwasawa domain". A proof of this containment was given by Huckleberry using complex analysis. By contrast, we need no complex analysis in this paper. In fact, we prove a theorem generalized for two associated symmetric subgroups in real Lie groups. Moreover, by the symmetry of two associated symmetric subgroups, we can also give a direct proof of the known fact that the Akhiezer-Gindikin domain D is contained in all cycle spaces. 
@article{JLT_2003_13_2_JLT_2003_13_2_a14,
     author = {T. Matsuki },
     title = {Stein {Extensions} of {Riemann} {Symmetric} {Spaces} and some {Generalization}},
     journal = {Journal of Lie theory},
     pages = {565--572},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2003},
     url = {http://geodesic.mathdoc.fr/item/JLT_2003_13_2_JLT_2003_13_2_a14/}
}
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T. Matsuki . Stein Extensions of Riemann Symmetric Spaces and some Generalization. Journal of Lie theory, Tome 13 (2003) no. 2, pp. 565-572. http://geodesic.mathdoc.fr/item/JLT_2003_13_2_JLT_2003_13_2_a14/