"Some mth-order Difference Sequence Spaces of Generalized Means and Compact Operators"

2013/07/19 by Amit Maji, Maji, Amit, Atanu Manna +3
Mathematics · #Approximation Theory and Sequence Spaces #Fixed Point Theorems Analysis #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.1307.5883

Abstract

In this paper, new sequence spaces X(r, s, t ;Δ^(m)) for X∈ \l_∞, c, c₀\ defined by using generalized means and difference operator of order m are introduced. It is shown that these spaces are complete normed linear spaces and the spaces c₀(r, s, t ;Δ^(m)), c(r, s, t ;Δ^(m)) have Schauder basis. Furthermore, the α-, β-, γ- duals of these spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from X(r, s, t ;Δ^(m)) to X. Finally, some classes of compact operators on the spaces c₀(r, s, t ;Δ^(m)) and l_∞(r, s, t ;Δ^(m)) are characterized by using the Hausdorff measure of noncompactness.

Citations

• On Certain Sequence Spaces

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