If the matrices {Ai}, ( I 0 such that for every r and M, there exists a v = v (r)> r such that (1), (2) and (3) cannot hold simultaneously for any finite set of sequences {xi,} (1 < i< N). Such values of e we shall call admissible. Let d be the set of bounded sequences limited by A, then the matrix B is b-stronger than A if N D sd and the two matrices are b-equivalent if = d . By d + .~ is denoted the set of bounded sequences s, s = x + y, where x e d , y ~ . The norm, h(A), of a regular matrix A=(am,,) is defined by, oo