Weaving frames are powerful tools in wireless sensor networks and pre-processing signals. In this paper, we introduce the concept of weaving for g-frames in Hilbert spaces. We first give some properties of weaving g-frames and present two necessary conditions in terms of frame bounds for weaving g-frames. Then we study the properties of weakly woven g-frames and give a sufficient condition for weaving g-frames. It is shown that weakly woven is equivalent to woven. Two sufficient conditions for weaving g-Riesz bases are given. And a weaving equivalent of an unconditional g-basis for weaving g-Riesz bases is considered. Finally, we present Paley–Wiener-type perturbation results for weaving g-frames.

中文翻译：

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关于希尔伯特空间的编织g框架

编织框架是无线传感器网络和预处理信号中的强大工具。在本文中，我们介绍了希尔伯特空间中g帧编织的概念。我们首先给出编织g帧的一些属性，并根据编织g帧的帧边界给出两个必要条件。然后，我们研究了弱编织g框架的性能，并为编织g框架提供了充分的条件。结果表明，弱编织等同于编织。给出了编织g-Riesz基的两个充分条件。并考虑了编织g-Riesz基的无条件g基的编织等价物。最后，我们提出了编织g框架的Paley–Wiener型摄动结果。