Geometric significance of Toeplitz kernels

摘要

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 L2. We also investigate this connection in the context of restricted Grassmann manifolds associated to p-Schatten ideals and essentially commuting projections. (C) 2018 Elsevier Inc. All rights reserved.