Arkiv för Matematik

  • Ark. Mat.
  • Volume 12, Number 1-2 (1974), 41-49.

Every sequence converging to O weakly in L2 contains an unconditional convergence sequence

János Komlós

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Note

Throughout the paper all functions are measurable functions on some measure space {X, S, μ}. It is clear that it is sufficient to prove our Theorem in case of finite measure, thus we can take μ(X)=1.

As a rule, we do not indicate the arguments of functions: writing ϕ, f etc. instead of ϕ(x), f(x) etc., and μ(f>λ) instead of μ({x; f(x)>λ}), and the measure: writing ∫ ϕ, ∫ ϕ1ϕ2 etc. instead of Xϕ1(x)ϕ2(x)μ(dx) etc.; we also say «almost everywhere» instead of «μ-almost everywhere». $\alpha _n \mathop \rightharpoonup \limits_{L_p } \alpha $ will stand for weak convergence in LP.

Article information

Source
Ark. Mat., Volume 12, Number 1-2 (1974), 41-49.

Dates
Received: 7 December 1972
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485896190

Digital Object Identifier
doi:10.1007/BF02384745

Mathematical Reviews number (MathSciNet)
MR346412

Zentralblatt MATH identifier
0279.40001

Rights
1974 © Institut Mittag-Leffler

Citation

Komlós, János. Every sequence converging to O weakly in L 2 contains an unconditional convergence sequence. Ark. Mat. 12 (1974), no. 1-2, 41--49. doi:10.1007/BF02384745. https://projecteuclid.org/euclid.afm/1485896190


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