Generalized Hausdorff Matrices Research Articles

Concerning Hausdorff matrices and absolutely convergent sequences

for'} =0,1, 2,) This paper is concerned with the determination of those generalized Hausdorff matrices which sum all absolutely convergent sequences. Theorem 2 gives a sufficiency condition stated in terms of the behavior of the points of continuity of the graph of g and Theorems 3 and 4 provide examples which serve to further describe functions which generate such matrices. Theorem 5 gives a necessary and sufficient condition in terms of moment sequences. Theorem 1 gives conditions which are necessary and sufficient for a semi-infinite complex number matrix to sum all absolutely convergent sequences and although the theorem is known [31, a brief proof is included here for completeness since the author does not know of one in the literature.