Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-16T23:55:28.372Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Billard, P., Kwapień, S., Pelczyński, A. and Samuel, C.. Biorthogonal systems of random unconditional convergence in Banach spaces. Texas Functional Analysis Seminar 1985–1986, 13–35.Google Scholar
[2]Kwapień, S. and Pelczyński, A.. The main triangle projection in matrix spaces and its application. Studia Math. 34 (1970), 43–68.CrossRefGoogle Scholar
[3]Lindenstrauss, J. and Tzafriri, L.. Classical Banach spaces, vols. 1 and 2 (Springer-Verlag, 1977 and 1979).CrossRefGoogle Scholar
[4]Maurey, B. and Pisier, G.. Séries de variables aléatoires vectorielles indépendantes et propriétés géometriques des espaces de Banach. Studia Math. 58 (1976), 45–90.CrossRefGoogle Scholar
[5]Pelczyński, A.. All separable Banach spaces admit for every ε > 0 fundamental and total biorthogonal sequences bounded by 1 + ε. Studia Math. 55 (1976), 295–304.CrossRefGoogle Scholar
[6]Singer, T.. Bases in Banach Spaces, vol. 1 (Springer-Verlag, 1970).CrossRefGoogle Scholar
[7]Wojtaszczyk, P.. Every separable Banach space containing c 0 has a RUC-system. Texas Functional Analysis Seminar 1985–1986, 37–39.Google Scholar