XXXIX Workshop on Geometric Methods in Physics 27.06-3.07.2021
IX School on Geometry and Physics 21-25.06.2021

Esteban Andruchow

Grassmann geometry in spaces of functions

The condition for the existence of a geodesic of the Grassmann manifold between two closed subspaces $S$, $T$ of a Hilbert space $H$, is that $\dim(S\cap T^\perp)=\dim(S^\perp\cap T)$. The geodesic is unique if these dimensions are zero. We study these conditions in spaces of functions. Moreover, such geodesic has minimal length for the metric induced by the usual norm of operators (when one parametrizes the Grassmann manifold as orthogonal projecions). This in turn provides interesting operator inequalities in the aforementioned spaces.

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University of Bialystok

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