Abstract
Let \({\widetilde{L}_p(\mathcal{M})}\) be the space of all bounded \({L_p(\mathcal{M})}\) -quasi-martingales and \({\widetilde{\mathcal{H}}_p(\mathcal{M})}\) the Hardy space of noncommutative quasi-martingales. Then
with equivalent norms for 1 < p < ∞ and p −1 + q −1 = 1, where \({BD_q(\mathcal{M})}\) is a subspace of \({l_\infty (L_q(\mathcal{M}))}\) and \({\mathcal{S}_q(\mathcal{M})}\) is a kind of space which is like but bigger than \({\widetilde{\mathcal{H}}_q(\mathcal{M})}\). The results for the case of p = 1 are also obtained.
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This work was supported by National Natural Science Foundation of China (11271293, 11471251) and the Research Fund for the Doctoral Program of Higher Education of China (2014201020205).
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Hou, YL., Ma, CB. Duality theorems for noncommutative quasi-martingale spaces. Acta Math. Hungar. 148, 132–146 (2016). https://doi.org/10.1007/s10474-015-0549-y
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DOI: https://doi.org/10.1007/s10474-015-0549-y