ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46B45; 46B32; 47B37 Fourie, Jan, Potchefstroom University, South Africa On convergence of sections of weakly p-summable sequences. We discuss an elementary proof (without representations) of the known fact that each element of the Banach space ℓ_{w}^{p}(X) of weakly absolutely psummable sequences (if 1 ≤ p < ∞) in the Banach space X is the norm limit of its n’th sections if and only if each absolutely p-summable sequence in X is a norm null sequence. The proof makes use of elementary sequence space properties only. 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.