|XXXIX Workshop on Geometric Methods in Physics||28.06-4.07.2020|
|IX School on Geometry and Physics||22-26.06.2020|
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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