General K-closedness results in noncommutative Lebesgue spaces and applications to the real interpolation of noncommutative martingale Hardy spaces

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.
非交换勒贝格空间中的一般K封闭性结果及其在非交换马丁格哈代空间实插值中的应用
在本文中,我们在涉及滤波的非交换 Lebesgue 空间实插值的背景下,建立了一个新的一般 $K$ 闭合性结果。作为应用,我们推导了各类非交换马氏哈代空间的 $K$ 闭合性结果,解决了兰德里安托阿尼纳提出的一个问题。对这一一般结果的证明,采用了布尔干的方法,在非交换马汀形的框架内,对圆盘上的经典哈代空间进行实插。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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