Some Hausdorff matrices not of type M

Commutants of some Hausdorff matrices

“…B is obtained by removing the first row and first column from A -a oo l. Therefore B = U*DU. By Theorem 1 of [4], D is not of type M, and a suitable sequence t is t 0 = 1, t n = (-ϊ) n ε(e -1) (e -n + l)/n I n > 0. Therefore B is also not of type M.…”

Correction to: “Commutants of some Hausdorff matrices”

“…(2) (U*) n+1 (A -a n J)U n+1 of type M for each n is equivalent to 618 (1). This assertion is false.…”

“…In [2] it is shown that, for A a conservative triangle, B a matrix with finite norm commuting with A, B is triangular if and only if (1) for each tel and each n, t(Aa nn I) -0 implies t belongs to the linear span of (β 0 , e u •••, e n ). On page 716 of [2] it is asserted that…”

“…Then, for each n f A -a nn l = (Z7*) n+1 (Aa n J)U n+ί = B, where b nn = 0 for each n, and b nk = a nk otherwise. The only solutions of tB = 0 for tel lie in the linear span of e 0 , so that A satisfies (1). However, B is not of type M.…”

Corrections to: “Versum sequences in the binary system”

“…We can regard H as the product of two Hausdorίf matrices H a and H β , with generating sequences a n = (n -1/2)/(n + 1) and β n = n/{n + 2), respectively. From Theorem 1 of [1], the sequence t = {t n }, with t 0 = 1; t n = (-l) % (l/2)(-3/2). -(-n + 3/2)/%!, n > 0 satisfies ίfi α = 0.…”