On convergence of sections of sequences in Banach spaces
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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.
Key words and phrasesweakℓp-sequences Orlicz sequence spaces compact operators
1991 Mathematics Subject Classification46B45 46A32 47B37
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- Diestel J.,Sequences and Series in Banach Spaces, Springer-Verlag, New York, 1984.Google Scholar