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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.

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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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Authors and Affiliations

  1. Department of Mathematics, Samara National Research University, Moskovskoye Shosse 34, Samara, Russia, 443086

    Sergey V. Astashkin

  2. Facultad de Matemáticas, Instituto de Matemáticas (IMUS), Universidad de Sevilla, Calle Tarfia s/n, 41012, Sevilla, Spain

    Guillermo P. Curbera

Authors
  1. Sergey V. Astashkin
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  2. Guillermo P. Curbera
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Corresponding author

Correspondence to Sergey V. Astashkin.

Additional information

The work of the first author was supported by the Ministry of Education and Science of the Russian Federation, project 1.470.2016/1.4 and by the RFBR Grant 17-01-00138.

The second author acknowledges the support of MTM2015-65888-C4-1-P, MINECO (Spain).

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Astashkin, S.V., Curbera, G.P. Random unconditional convergence and divergence in Banach spaces close to \(L^1\) . Rev Mat Complut 31, 351–377 (2018). https://doi.org/10.1007/s13163-017-0249-y

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  • DOI: https://doi.org/10.1007/s13163-017-0249-y

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