First, a characterization of K-dual frames of a K-frame is given. Two types of K-frames are also identified whose corresponding K-dual frames may enjoy some well-ordered frames. Second, an operator process is tested to the results given in Jia and Zhu (Results Math 73(4):138, 2018) and Ramu and Johnson (SeMA J 73(2):171–181, 2016). The approach directs us to obtain the same results more straightforward under relatively weaker conditions.

中文翻译：

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K-Frames 上的求和和对偶运算

首先，给出了K帧的K对偶帧的特征。还确定了两种类型的K帧，其对应的K对偶帧可以享受一些有序的帧。其次，根据 Jia 和 Zhu (Results Math 73(4):138, 2018) 和 Ramu and Johnson (SeMA J 73(2):171–181, 2016) 中给出的结果测试算子过程。该方法指导我们在相对较弱的条件下更直接地获得相同的结果。