Research Article Open Access

The Banach space mp(X), for 1 ≤ p <8 has the Banach-Saks Property

Naim L. Braha

Abstract

Problem statement: In the theory of Banach spaces one of the problems which describes geometric property of Banach spaces is Banach-Saks Property. In this context we were known many Banach spaces which had this property such as Lp[0, 1] for 1 < p ≤ 2. Approach: Following the sequential structure of the Banach sequence space mp(X), for 1  ≤ p < 8, defined in[1], we arrived to describe a geometric property of this Banach spaces. Results: In this note we showed that Banach spaces mp(X), for 1  ≤ p < 8 had the Banach-Saks Property. Conclusion/Recommendations: Based in present approach, we recommend using our method to study the weak Banach-Saks property in sequential Banach spaces.

Journal of Mathematics and Statistics
Volume 5 No. 1, 2009, 63-64

DOI: https://doi.org/10.3844/jmssp.2009.63.64

Submitted On: 12 September 2007 Published On: 31 March 2009

How to Cite: Braha, N. L. (2009). The Banach space mp(X), for 1 ≤ p <8 has the Banach-Saks Property. Journal of Mathematics and Statistics, 5(1), 63-64. https://doi.org/10.3844/jmssp.2009.63.64

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Keywords

  • Banach-saks property
  • scalar sequences