Canonical Dual $$\varvec{K}$$K-g-Bessel Sequences and $$\varvec{K}$$K-g-Frame Sequences
Canonical Dual $$\varvec{K}$$K-g-Bessel Sequences and $$\varvec{K}$$K-g-Frame Sequences
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DOI：
10.1007/s00025-018-0776-y
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发表时间：
2018-02
影响因子：
2.2
通讯作者：
Zhong-Qi Xiang
中科院分区：
文献类型：
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作者：
Zhong-Qi Xiang
aK-g-框架的经典典范对偶是不存在的，因为框架算子可能不是可逆的。引入了典型对偶K-g-Bessel序列的概念，研究了K-g-框架的对偶性，它具有与经典对偶K-g-Bessel序列相似的性质.得到了ParsevalK-g-框架的标准对偶K-g-Bessel序列的精确形式及其它相关结果。我们还引入了K-g-框架序列的概念来研究局部K-g-框架的性质。给出了一个K-g-框架序列是K-g-框架的充要条件，以及一个有界算子序列是K-g-框架序列的充要条件.最后，我们研究了K-g-框架序列与闭子空间的g-框架之间的关系，以及两个K-g-框架序列与所涉及算子的值域之间的关系。
The classical canonical dual for aK-g-frame is absent since the frame operator may not be invertible. We introduce the concept of canonical dualK-g-Bessel sequences, which have some properties similar to classical canonical dual, to investigate the duality ofK-g-frames. We obtain the exact form of the canonical dualK-g-Bessel sequences for ParsevalK-g-frames and some other related results. We also introduce the concept ofK-g-frame sequences to explore the properties of localK-g-frames. We present a necessary and sufficient condition under which aK-g-frame sequence is aK-g-frame, and necessary and sufficient conditions for a sequence of bounded operators to be aK-g-frame sequence. We end the paper by examining the relationship betweenK-g-frame sequences and g-frames for closed subspaces, and the relationship between twoK-g-frame sequences and the ranges of the involved operators.