Some new sequence spaces derived by the domain of generalized difference matrix
Let ? ? denote any one of the classical spaces ?? ? ? , c c , c0 c 0 and ?p ? p of bounded, convergent, null and absolutely p p -summable sequences, respectively, and ? ? also be the domain of the generalized difference matrix B(r,s) B ( r , s ) in the sequence space ? ? , where 1?p<? 1 ? p < ? . The present paper is devoted to studying on the sequence space ? ? . Furthermore, the ? ? - and ? ? -duals of the space ? ? are determined, and 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. Finally, the classes ( ? ? 1 : ? 2 ) and ( ? ? 1 : ? ? 2 ) of infinite matrices are characterized, where ?1?{??,c,c0,?p,?1} ? 1 ? { ? ? , c , c 0 , ? p , ? 1 } and ?2?{??,c,c0,?1} ? 2 ? { ? ? , c , c 0 , ? 1 } .
matrix domain of a sequence space ? ? - and ? ? -duals ? ? ? ? ? ? ? ? ? ? schauder basis and matrix transformations