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Quasi-martingale Inequalities in Noncommutative Symmetric Spaces

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Abstract

In this paper, we prove Doob’s inequality and Burkholder–Gundy inequalities for quasi-martingales in noncommutative symmetric spaces. We also consider the inclusion relations between \(\widetilde{\mathcal {H}}_E(\mathcal {M})\) and \(\widetilde{h}_{E}(\mathcal {M})\), where \(\widetilde{\mathcal {H}}_E(\mathcal {M})\) and \(\widetilde{h}_{E}(\mathcal {M})\) are the Hardy spaces of quasi-martingales in noncommutative symmetric spaces.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Xinxiang University, Xinxiang, Henan, People’s Republic of China

    Congbian Ma

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, People’s Republic of China

    Youliang Hou

Authors
  1. Congbian Ma
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  2. Youliang Hou
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Corresponding author

Correspondence to Congbian Ma.

Additional information

Communicated by Mohammad Sal Moslehian.

This work was supported by National Natural Science Foundation of China (11471251, 11671308).

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Ma, C., Hou, Y. Quasi-martingale Inequalities in Noncommutative Symmetric Spaces. Bull. Malays. Math. Sci. Soc. 42, 2639–2655 (2019). https://doi.org/10.1007/s40840-018-0621-1

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  • DOI: https://doi.org/10.1007/s40840-018-0621-1

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