## Abstract

Let ${\stackrel{\u02c6}{L}}_{p}\left(\mathrm{M}\right)$ be the space of bounded ${L}_{p}\left(\mathrm{M}\right)$-quasimartingales. We prove that, with equivalent norms, $\left({\stackrel{\u02c6}{L}}_{{p}_{0}}\right(\mathrm{M}),{\stackrel{\u02c6}{L}}_{{p}_{1}}(\mathrm{M}){)}_{\theta ,p}={\stackrel{\u02c6}{L}}_{p}(\mathrm{M})$, where $1<{p}_{0},{p}_{1}\le \infty $, $1<\theta <1$, and $\frac{1}{p}=\frac{1-\theta}{{p}_{0}}+\frac{\theta}{{p}_{1}}$. We also prove that, for $1<p<q<\infty $, $\left({\stackrel{\u02c6}{BMO}}^{c}\right(\mathrm{M}),{\stackrel{\u02c6}{\mathrm{H}}}_{p}^{c}(\mathrm{M}){)}_{\frac{p}{q},q}={\stackrel{\u02c6}{\mathrm{H}}}_{q}^{c}(\mathrm{M})$ and $\left({\stackrel{\u02c6}{BMO}}^{r}\right(\mathrm{M}),{\stackrel{\u02c6}{\mathrm{H}}}_{p}^{r}(\mathrm{M}){)}_{\frac{p}{q},q}={\stackrel{\u02c6}{\mathrm{H}}}_{q}^{r}(\mathrm{M})$, where ${\stackrel{\u02c6}{\mathrm{H}}}_{p}\left(\mathrm{M}\right)$ and $\stackrel{\u02c6}{BMO}\left(\mathrm{M}\right)$ are, respectively, the Hardy space and the bounded mean oscillation space of noncommutative quasimartingales.

## Citation

Congbian Ma. Youliang Hou. "Interpolation of noncommutative quasimartingale spaces." Ann. Funct. Anal. 7 (3) 484 - 495, August 2016. https://doi.org/10.1215/20088752-3624877

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