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Zbl 1029.46012
Mursaleen
Some geometric properties of a sequence space related to $\ell^p$. (English)
[J] Bull. Aust. Math. Soc. 67, No.2, 343-347 (2003). ISSN 0004-9727

This paper is devoted to the Hausdorff measure of noncompactness of any bounded subset $m(\varphi)$, introduced and studied by W. L. C. Sargent. The author obtains an explicit formula for the Hausdorff measure. Moreover, the author studies also some geometric properties of $m (\varphi)$, showing that a geometric constant $C(X)$ related to the Banach-Saks property is equal to 2 for $X=\{m (\varphi)\}$.
[Messoud Efendiev (Berlin)]

MSC 2000:: *46B20 Geometry and structure of normed spaces
46E30 Spaces of measurable functions

Keywords: Hausdorff measure of noncompactness; Banach-Saks property

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