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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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