Geodesic
The Extent of the Sequence Space Associated with a Basis
Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 636-641

Voir la notice de l'article provenant de la source Cambridge University Press

The associated sequence space S of a sequence of vectors {xn } in a Banach space consists of all scalar sequences (sn ) for which converges. My primary motivation in writing this paper was to present a new proof to a recent theorem of N. I. and V. I. Gurarii concerning limits of extent on S when {xn } is a basis of a uniformly convex or a uniformly smooth Banach space [5], This theorem is stated as Theorem 2.4. Several interesting consequences of this theorem were noted by N. I. Gurarii in [3] and [4]. 
Ruckle, William H. The Extent of the Sequence Space Associated with a Basis. Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 636-641. doi: 10.4153/CJM-1972-059-8
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