Abstract
An elementary proof of the (known) fact that each element of the Banach spaceℓ pw (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 pw (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.
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Aywa, S., Fourie, J.H. On convergence of sections of sequences in Banach spaces. Rend. Circ. Mat. Palermo 49, 141–150 (2000). https://doi.org/10.1007/BF02904225
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DOI: https://doi.org/10.1007/BF02904225