ABSTRACT
In this section we prove the main theorems concerning constructions of smooth structures on homogeneous spaces of general Banach-Lie groups. The most important result is that a quotient of a Banach-Lie group by a BanachLie subgroup is always a smooth homogeneous space (Theorem 4.19). We also discuss the notion of algebraic subgroup, which is helpful in order to produce concrete examples of Banach-Lie subgroups.
