Banach-Lie groupoids and generalized inversion (Q1712595)

The authors develop a basic theory of Banach-Lie groupoids and algebroids, adapting some classical results on classical finite dimensional Lie groupoids. They illustrate it by a brief discussion on its relation to some differentiability questions in the theory of C*-algebras. They study in particular locally transitive Banach-Lie groupoids, a class of groupoids that play a central role in the description of the differentiability properties of the Moore-Penrose pseudo-inverse in C*-algebras.