The Banach space mp(X), for 1 ≤ p <8 has the Banach-Saks Property
Naim L. Braha
DOI : 10.3844/jmssp.2009.63.64
Journal of Mathematics and Statistics
Volume 5, Issue 1
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, 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.
© 2009 Naim L. Braha. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.