Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-07-01T03:06:42.826Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  24 October 2008

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

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
Copyright
Copyright © Cambridge Philosophical Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Beauzamy, B. and Lapresté, J. T.. Modèles Étalés des Espaces de Banach (Hermann, 1984).Google Scholar
[2]Carne, T., Cole, B. and Gamelin, T.. A uniform algebra of analytic functions on a Banach space. Trans. Amer. Math. Soc. 314 (1989), 639659.Google Scholar
[3]Castillo, J. M. F. and Sánchez, F.. Weakly p-compact, p-Banach–Saks and super-reflexive Banach spaces. J. Math. Anal. Appl., to appear.Google Scholar
[4]Cembranos, P.. The hereditary Dunford–Pettis property on C(K, E). Illinois J. Math. 31 (1987), 365373.Google Scholar
[5]Cembranos, P.. The hereditary Dunford–Pettis property for l 1(E). Proc. Amer. Math. Soc. 108 (1990), 947950.Google Scholar
[6]Diestel, J.. A survey of results related to the Dunford-Pettis property. In Contemporary Mathematics, vol. 2 (American Mathematical Society, 1980), pp. 1560.Google Scholar
[7]Johnson, W. B.. On quotients of Lp which are quotients of lp. Compositio Math. 34 (1977), 6989.Google Scholar
[8]Jaramillo, J. and Prieto, A.. On the weak polynomial convergence on a Banach space. Proc. Amer. Math. Soc., to appear.Google Scholar
[9]Knaust, H. and Odell, E.. On co-sequences in Banach spaces. Israel J. Math. 67 (1989), 153169.CrossRefGoogle Scholar
[10]Knaust, H. and Odell, E.. Weakly null sequences with upper lp-estimates. In Functional Analysis, Lecture Notes in Math. vol. 1470 (Springer-Verlag, 1991), pp. 85107.CrossRefGoogle Scholar
[11]Partington, J. R.. On the Banach-Saks property. Math. Proc. Cambridge Philos. Soc. 82 (1977), 369374.Google Scholar
[12]Schachermayer, W.. The Banach–Saks property is not L 2-hereditary. Israel J. Math. 40 (1981), 340344.Google Scholar