Assuming the existence of certain large cardinal numbers, we prove that for every projective filter $\mathcal{F}$ over the set of natural numbers, $\mathcal{F}$‐bases in Banach spaces have continuous coordinate functionals. In particular, this applies to the filter of statistical convergence, thereby we solve a problem by Kadets (at least under the presence of certain large cardinals). In this setting, we recover also a result of Kochanek (Studia Math., 2012) who proved continuity of coordinate functionals for countably generated filters.

中文翻译：

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大基数和Banach空间中过滤基的协调功能的连续性

假设存在某些大基数，我们证明对于每个射影滤波器 $\mathcal{F}$ 在一组自然数上 $\mathcal{F}$Banach空间中的基础具有连续的坐标功能。特别是，这适用于统计收敛的过滤器，从而我们通过Kadets（至少在某些大基数的存在下）解决了问题。在这种情况下，我们还恢复了Kochanek（Studia Math。，2012）的结果，该结果证明了可数生成的过滤器的坐标函数的连续性。