Domain of the double sequential band matrix in the classical sequence spaces

Abstract

Let denote any one of the classical spaces , c, c 0 and p of bounded, convergent, null and absolutely p-summable sequences, respectively, and also be the domain of the double sequential band matrix B( r, s) in the sequence space , where (r n ) n=0 and (s n ) n=0 are given convergent sequences of positive real numbers and 1 p < . The present paper is devoted to studying the sequence space . Furthermore, the and -duals of the space are determined, the Schauder bases for the spaces c, c 0 and p are given, and some topological properties of the spaces c 0 , 1 and p are examined.