Measures of Noncompactness in N(p,q) Summable Sequence Spaces

2018/05/07 by Malik, Ishfaq Ahmad, Jalal, Tanweer
#40H05 #46A45 #47B07 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1805.03960

Abstract

In this paper we first define the N(p,q) summable sequence spaces and obtain some basic results related to these spaces. The necessary and sufficient conditions for infinite matrices A to map these spaces on X~~,~~X=c₀, c or ℓ_∞ is obtained and Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of linear operators defined on these spaces.

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