This paper mainly divided into two parts. The first part gives same facts about topological properties of certain linear topological spaces, inclusion relations and matrix mappings. The second part establishes some identities or estimates for the matrix operator norms and the Hausdorff measures of noncompactness of certain matrix operators, characterize some classes of compact operators on these spaces.
"On generalized weighted means and compactness of matrix operators." Ann. Funct. Anal. 6 (3) 8 - 28, 2015. https://doi.org/10.15352/afa/06-3-2