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Article: The Banach space [m.sub.p](X), for 1 [less than or equal to] p < 8 has the Banach-Saks Property.
- Article from:
- Journal of Mathematics and Statistics
- Article date:
- January 1, 2009
- Author:
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INTRODUCTION
The Banach-Saks property was studied in Banach spaces and several characterizations were given for it. In [5], was studied Banach-Saks property in the product of Banach spaces. Another characterizations was studied taking into consideration the Haar null sets property in sense of Christensen [4]. In this note we prove that the Banach space [m.sub.p](X), for 1 [less than or equal to] p
[conjunction] = {a = ([a.sub.i]): ([a.sub.i]) [member of] R}
(Alternatively, we may also take [conjunction] to be the vector space of complex scalar sequences and what follows remains true in both cases, real and complex). The space [m.sub.p](X) is defined as:
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