On ( ) -di erence sequence spaces using generalized means and compact operators Abstract: In this paper, sequence spaces ( , , ; ( ) ) for ∈ { ∞ , , 0 } are introduced by combining the generalized means and the -th order generalized di erence operator ( ) ( , ). It is shown that these spaces are complete normed linear spaces and the spaces 0 ( , , ; ( ) ), ( , , ; ( ) ) have Schauder bases. Furthermore, the -, -, -duals of these spaces are computed. The necessary and sucient conditions for some matrix transformations from ( , , ; ( ) ) to , where , ∈ { ∞ , , 0 }, are also obtained. Finally, some classes of compact operators on the spaces ( , , ; ( ) ) for ∈ { ∞ , , 0 } are characterized by using the Hausdor measure of noncompactness.
PreliminariesLet ∞ , and 0 be the spaces of all bounded, convergent and null sequences = ( ), respectively, with the norm ‖ ‖ ∞ = sup | |. Let and be the sequence spaces of all bounded and convergent series, respectively. We write = (1, 1, . . .) Brought to you by | Purdue University Libraries Authenticated Download Date | 6/20/15 1:55 PM On ( ) -di erence sequence spaces