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

Abstract

In this paper we first recall some properties of triangle Toeplitz matrices of the Banach algebra Sr associated with power series. Then for boolean Toeplitz matrices M we explicitly calculate the product MN that gives the number of ways with N arcs associated with M. We compute the matrix BN (i, j), where B (i, j) is an infinite matrix whose the nonzero entries are on the diagonals m &#8722; n = i or m &#8722; n = j. Next among other things we consider the infinite boolean matrix B+&#8734; that have infinitely many diagonals with nonzero entries and we explicitly calculate (B+&#8734;)N. Finally we give necessary and sufficient conditions for an infinite matrix M to map c (BN (i, 0)) to c.</p