On convergence of sections of sequences in Banach spaces |
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Authors: | Shem Aywa and Jan H. Fourie |
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Affiliation: | (1) Department of Mathematics and Applied Mathematics, Potchefstroom University for C.H.E., 2520 Potchefstroom, South Africa |
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Abstract: | An 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. |
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Keywords: | KeywordHeading" > and phrases weakℓ p-sequences Orlicz sequence spaces compact operators |
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