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RUC-systems and Besselian systems in Banach spaces

Published online by Cambridge University Press:  24 October 2008

D. J. H. Garling  and
N. Tomczak-Jaegermann
D. J. H. Garling
Affiliation:
St John's College, Cambridge
N. Tomczak-Jaegermann
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Canada
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Extract

Let (rj) be a Rademacher sequence of random variables – that is, a sequence of independent random variables, with , for each j. A biorthogonal system in a Banach space X is called an RUC-system[l] if for every x in [ej] (the closed linear span of the vectors ej), the series

converges for almost every ω. A basis which, together with its coefficient functionals, forms an RUC-system is called an RUC-basis. A biorthogonal system is an RLTC-svstem if and only if there exists 1 ≤ K < ∞ such that

for each x in [ej]: the RUC-constant of the system is the smallest constant K satisfying (1) (see [1], proposition 1.1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 1 , July 1989 , pp. 163 - 168
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

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