Let C-n = L + W be a given direct sum decomposition. We determine the large
st number r(i) such that all subspaces M for which the gap theta between L
and M satisfies theta(L, M) < r(i) have the property dim(M boolean AND W) <
i. The problem involves angles be tween subspaces, i.e. singular values of
products of projections. (C) 1999 Elsevier Science Inc. All rights reserve
d.