Daniel Beltita
Groupoid techniques in Hilbert space operator theory
We study the action of the groupoid of partial isometries on the set of normal operators with respect to the moment map given by the range projection.The corresponding groupoid orbits turn out to have Banach manifold structures for which the target map is a smooth submersion. We also describe the norm closure of the groupoid orbit of any normal operator and we investigate the way its topological or differentiable structures are encoded by the spectral properties of the operator under consideration. The presentation is based on joint work with Gabriel Larotonda.
