Author： Vershynin R.
Publisher： Taylor & Francis Ltd
ISSN： 1607-3606
Source： Quaestiones Mathematicae, Vol.23, Iss.1, 2000-03, pp. : 87-98
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Abstract
An absolutely representing system (ARS) in a Banach space X is a set D ⊂ X such that every vector x in X admits a representation by an absolutely convergent series x = Σi aixi with (ai) ⊂ R and (xi) ⊂ D. We investigate some general properties of absolutely representing systems. In particular, absolutely representing systems in uniformly smooth and in B-convex Banach spaces are characterized via ε-nets of the unit balls. Every absolutely representing system in a B-convex Banach space is quick, i.e., in the representation above one can achieve ∥aixi∥ < cqi ∥x∥, i = 1, 2,… for some constants c > 0 and q ∈ (0,1).
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