Revista Matemática Complutense

, Volume 31, Issue 2, pp 351–377 | Cite as

Random unconditional convergence and divergence in Banach spaces close to \(L^1\)

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Abstract

We study conditions on Banach spaces close to \(L^1\) guaranteeing the existence of Random Unconditional Convergence and Divergence systems. Special attention is given to the Haar system and to Cesàro spaces.

Keywords

Random unconditional convergence Schauder basis Haar functions Rearrangement invariant space Cesàro spaces 

Mathematics Subject Classification

Primary 46E30 46B15 Secondary 46B09 

Notes

Acknowledgements

The authors would like to thank Konstantin Lykov and Konstantin Tikhomirov for fruitful discussions at the early stages of this research. The first author acknowledges the support and hospitality of the Instituto de Matemáticas de la Universidad de Sevilla (IMUS).

We thank the referee for providing very useful suggestions.

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Copyright information

© Universidad Complutense de Madrid 2017

Authors and Affiliations

  1. 1.Department of MathematicsSamara National Research UniversitySamaraRussia
  2. 2.Facultad de Matemáticas, Instituto de Matemáticas (IMUS)Universidad de SevillaSevillaSpain

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