# Eduardo Chiumiento

## Geometric approach to the Moore-Penrose inverse and polar decomposition in operator ideals

In this talk we consider three fundamental maps in matrix analysis and operator theory: the Moore-Penrose inverse, the operator modulus, and the polar factor arising in the polar decomposition. We work in an infinite-dimensional setting, where we use norms given by symmetrically-normed ideals, and the notion of index of a pair of projections. We will show that the Moore-Penrose inverse is a real binalytic map between homogeneous spaces of Lie-Banach groups associated with symmetrically-normed ideals. Furthermore, the maps given by the operator modulus and polar factor are real analytic fiber bundles. This is based on a recent joint work with Pedro Massey (IAM-UNLP).