Geometric significance of Toeplitz kernels
  Let $L^2$ be the Lebesgue space of square-integrable functions on the unit circle. We show that the injectivity problem for Toeplitz operators is linked to the existence of geodesics in the Grassmann manifold of $L^2$. We also investigate this connection in the context of restricted Grassmann manifolds associated to $p$-Schatten ideals and essentially commuting projections. 
Esteban Andruchow, Eduardo Chiumiento, Gabriel Larotonda
math.FA math-ph math.DG math.MP math.OA