Some Fibonacci sequence spaces of non-absolute type derived from ℓ_p with (1 ≤ p ≤ ∞) and Hausdorff measure of non-compactness of composition operators

2017/06/18 by Anupam Das, Bipan Hazarika, Das, Anupam +3
Mathematics · Decision Sciences · #Approximation Theory and Sequence Spaces #Mathematical Analysis and Transform Methods #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.1706.07289

Abstract

The aim of the paper is to introduce the spaces ℓ_∞^λ(\widehatF) and ℓ_p^λ(\widehatF) derived by the composition of the two infinite matrices Λ=(λ_nk) and \widehatF=( f_nk ), which are the BK-spaces of non-absolute type and also derive some inclusion relations. Further, we determine the α-, β-, γ-duals of those spaces and also construct the basis for ℓ_p^λ(\widehatF). Additionally, we characterize some matrix classes on the spaces ℓ_∞^λ(\widehatF) and ℓ_p^λ(\widehatF). We also investigate some geometric properties concerning Banach-Saks type p. Here we characterize the subclasses K(X:Y) of compact operators, where X∈\ℓ_∞^λ(\widehatF),ℓ_p^λ(\widehatF)\ and Y∈\c₀,c, ℓ_∞, ℓ₁, bv\ by applying the Hausdorff measure of non-compactness, and 1≤ p

Related

• Some new Fibonacci difference spaces of non-absolute type and compact operators
• Some new Fibonacci difference spaces of non-absolute type and compact operators
• Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers
• Measures of Noncompactness in N(p,q) Summable Sequence Spaces
• On the spaces of λ- convergent and bounded series