INFINITE MATRICES ASSOCIATED WITH POWER SERIES AND APPLICATION TO OPTIMIZATION AND MATRIX TRANSFORMATIONS

In this paper we first recall some properties of triangle Toeplitz matrices of the Banach algebra S_r associated with power series. Then for boolean Toeplitz matrices M we explicitly calculate the product M^N that gives the number of ways with N arcs associated with M. We compute the matrix B^N (i, j), where B (i, j) is an infinite matrix whose the nonzero entries are on the diagonals m − n = i or m − n = j. Next among other things we consider the infinite boolean matrix B⁺_∞ that have infinitely many diagonals with nonzero entries and we explicitly calculate (B⁺_∞)^N. Finally we give necessary and sufficient conditions for an infinite matrix M to map c (B^N (i, 0)) to c.