Aywa, Shem.Fourie, Jan H.2019-05-062019-05-062000-02-01http://erepository.kibu.ac.ke/handle/123456789/855An elementary proof of the (known) fact that each element of the Banach spaceℓ w p (X) of weakly absolutelyp-summable sequences (if 1≤p<∞) in the Banach spaceX is the norm limit of its sections if and only if each element ofℓ w p (X) is a norm null sequence inX, is given. Little modification to this proof leads to a similar result for a family of Orlicz sequence spaces. Some applications to spaces of compact operators on Banach sequence spaces are considered.enAttribution-NonCommercial-ShareAlike 3.0 United Stateshttp://creativecommons.org/licenses/by-nc-sa/3.0/us/Weak-sequencesOrlicz sequence spacesCompact operatorsArticle