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arXiv · 2407.12335

K-closedness results in noncommutative Lebesgue spaces with filtrations

Hugues Moyart
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Abstract

In this paper, we establish a new general $K$-closedness result in the context of real interpolation of noncommutative Lebesgue spaces involving filtrations. As an application, we derive $K$-closedness results for various classes of noncommutative martingale Hardy spaces, addressing a problem raised by Randrianantoanina. The proof of this general result adapts Bourgain's approach to the real interpolation of classical Hardy spaces on the disk within the framework of noncommutative martingales.

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BibTeXRIS

Hugues Moyart. 2024-07-17. K-closedness results in noncommutative Lebesgue spaces with filtrations. https://doi.org/10.1016/j.jfa.2025.110829

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