Matrix Domains in Sequence Spaces

Abstract

This chapter is devoted to the domains of some particular summability matrices, with a special emphasize on the Cesàro, difference, m^th-order difference, Euler, Riesz and weighted mean sequence spaces, and other spaces derived in this way. Also, the Schauder bases of those spaces, their α-,fi β-, γ- duals, and the characterizations of some matrix transformations are given.

Keywords: Domain of an infinite matrix, Cesàro, difference, Euler, Riesz, generalized difference and weighted mean sequence spaces and concerning dual methods, space of p-bounded variation sequences, Schauder bases, α-, β-, γ- duals of a matrix domain, characterization of the matrix transformations related to the matrix domains, paranormed difference sequence spaces and moduli, Orlicz functions.