Rendiconti del Circolo Matematico di Palermo

, Volume 49, Issue 1, pp 141–150 | Cite as

On convergence of sections of sequences in Banach spaces

  • Shem Aywa
  • Jan H. Fourie


An elementary proof of the (known) fact that each element of the Banach space 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 of 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 phrases

weakp-sequences Orlicz sequence spaces compact operators 

1991 Mathematics Subject Classification

46B45 46A32 47B37 


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Copyright information

© Springer 2000

Authors and Affiliations

  • Shem Aywa
    • 1
  • Jan H. Fourie
    • 1
  1. 1.Department of Mathematics and Applied MathematicsPotchefstroom University for C.H.E.PotchefstroomSouth Africa

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