Matrix Transformations in Sequence Spaces

Abstract

In this chapter, the matrix transformations in sequence spaces are studied and the characterizations of the classes of Schur, Kojima and Toeplitz matrices together with their versions for the series-to-sequence, sequence-to-series and series-to-series matrix transformations are given.

Keywords: Matrix transformations between sequence spaces, ordinary, absolute and strong summability, KOjima-Schur theorem, Silverman-Toeplitz theorem, Schur's theorem, algebra, normed and Banach algebra, characteristic of a matrix, sequence-to-sequence, series-to-sequence, series-to-series and sequence-to-series matrix transformations, dual summability methods, arithmetics, Cesàro, Euler, Riesz and Nörlund means, Taylor, Ar, Hausdor, Borel and Abel matrices.