Some Paranormed Difference Sequence Spaces of Order m Derived by Generalized Means and Compact Operators

2013/08/10 by Maji, Amit, Srivastava, P. D.
#46A45 #46B15 #46B50 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1308.2667

Abstract

We have introduced a new sequence space l(r, s, t, p ;Δ^(m)) combining by using generalized means and difference operator of order m. We have shown that the space l(r, s, t, p ;Δ^(m)) is complete under some suitable paranorm and it has Schauder basis. Furthermore, the α-, β-, γ- duals of this space is computed and also obtained necessary and sufficient conditions for some matrix transformations from l(r, s, t, p; Δ^(m)) to l_∞, l₁. Finally, we obtained some identities or estimates for the operator norms and the Hausdorff measure of noncompactness of some matrix operators on the BK space l_p(r, s, t ;Δ^(m)) by applying the Hausdorff measure of noncompactness.

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