We introduce the notion of a continuous Schauder frame for a Banach space. This is both a generalization of continuous frames for Hilbert spaces and a generalization of unconditional Schauder frames for Banach spaces. Furthermore, we generalize the properties shrinking and boundedly complete to the continuous Schauder frame setting, and prove that many of the fundamental James theorems still hold in this general context.

中文翻译：

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Banach空间的连续Schauder框架

我们介绍了用于Banach空间的连续Schauder框架的概念。这既是针对希尔伯特空间的连续框架的推广，又是针对Banach空间的无条件Schauder框架的推广。此外，我们将收缩的和无穷大的属性推广到连续的Schauder框架设置，并证明了许多基本的James定理在这种一般情况下仍然成立。