Canonical angles of unitary spaces and perturbations of direct complements Original Research Article

Let the field of complex numbersn = script capital l circled plus %plane1D;4B2; be a given direct sum decomposition. We determine the largest number ri such that all subspaces script capital m for which the gap θ between script capital l and %plane1D;4B2; satisfies θ(script capital lscript capital m) have the property dim (script capital m∩%plane1D;4B2;). The problem involves angles between subspaces, i.e. singular values of products of projections.