CONE INCLUSION NUMBERS

The introduction of cone inclusion numbers allows one to view seemingl y different problems from one general perspective. Using this perspect ive several new results are obtained, such as: (a) the distance consta nt for T-n circle times T-n, where T-n denotes the algebra of n x n st rictly upper triangular matrices, is bounded above by [log(2) n] + 1; (b) for every natural number n there exists an n x n partial correlati on matrix for which the largest possible minimal eigenvalue of a compl etion is 1-root[n/2]; and (c) the lowest possible entry-wise supremum norm among all n x n matrices that induce a norm one Schur map is 1/ro ot n.