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The Extent of the Sequence Space Associated with a Basis

Published online by Cambridge University Press:  20 November 2018

William H. Ruckle
William H. Ruckle*
Affiliation:
Clemson University, Clemson, South Carolina
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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].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 4 , August 1972 , pp. 636 - 641
Copyright
Copyright © Canadian Mathematical Society 1972

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