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Upper lp-estimates in vector sequence spaces, with some applications

Published online by Cambridge University Press:  24 October 2008

Jesús M. F. Castillo  and
Fernando Sánchez
Jesús M. F. Castillo
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, Avda. de Elvas s/n, 06071 Badajoz, Spain
Fernando Sánchez
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, Avda. de Elvas s/n, 06071 Badajoz, Spain
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Extract

In [11], Partington proved that if λ is a Banach sequence space with a monotone basis having the Banach-Saks property, and (Xn) is a sequence of Banach spaces each having the Banach-Saks property, then the vector sequence space ΣλXn has this same property. In addition, Partington gave an example showing that if λ and each Xn, have the weak Banach-Saks property, then ΣλXn need not have the weak Banach-Saks property.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 2 , March 1993 , pp. 329 - 334
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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