We introduce the concept of strategically reproducible bases in Banach spaces and show that operators which have large diagonal with respect to strategically reproducible bases are factors of the identity. We give several examples of classical Banach spaces in which the Haar system is strategically reproducible: multi-parameter Lebesgue spaces, mixed-norm Hardy spaces and most significantly the space L 1 . Moreover, we show the strategical reproducibility is inherited by unconditional sums.

中文翻译：

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战略上可重复的基础和因式分解属性

我们在 Banach 空间中引入了策略可再现基的概念，并表明相对于策略可再现基具有大对角线的算子是恒等式的因素。我们给出了几个经典 Banach 空间的例子，其中 Haar 系统在策略上是可重复的：多参数 Lebesgue 空间、混合范数 Hardy 空间和最重要的空间 L 1 。此外，我们表明无条件和继承了战略可重复性。