Measures of Noncompactness in $\bar{N}(p,q)$ Summable Sequence Spaces

Abstract

In this paper we first define the $\bar{N}(p,q)$ 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 $X,X=c_0,c\text{ or }{\ell }_{\infty }$ 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.

15 pages. arXiv admin note: substantial text overlap with arXiv:1804.10349