g-框架的一些新性质

郭训香

数学学报 ›› 2014, Vol. 57 ›› Issue (5) : 881-892.

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数学学报 ›› 2014, Vol. 57 ›› Issue (5) : 881-892. DOI: 10.12386/A2014sxxb0082
论文

g-框架的一些新性质

    郭训香
作者信息 +

Some New Properties of g-Frames

    Xun Xiang GUO
Author information +
文章历史 +

摘要

考虑了g-框架的一些新性质.首先把有关框架的投影方法推广到g-框架，并且建立了一个类似的该方法对g-框架有效的充分必要条件.然后研究了包含g-Riesz基的g-框架，得到了在某些条件下g-Riesz框架一定包含g-Riesz 基.我们提出了具有子g-框架性质的g-框架的概念，证明了在某些条件下具有子g-框架性质的g-框架一定包含一个g-Riesz基.最后得到了一些g-框架与其诱导出的框架之间的在某些限制条件下的等价性质.

Abstract

In this paper, some properties of g-frames are considered. Firstly, we generalize the projection methods for frames to g-frames and a similar if and only if condition for such method works is established. Then we study the g-frames which contain g-Riesz bases. We obtain that under some constraint g-Riesz frame contains a g-Riesz basis. We also introduce the conception of g-frames with sub-g-frame property and show that under some restriction g-frame with sub-g-frame property contains a g-Riesz basis. Finally, we get several equivalent properties between g-frames and frames induced by the g-frames under some assumptions.

关键词

g-框架 / g-Riesz基 / g-Riesz框架 / 子g-框架性质 / g-线性无关

Key words

g-frame / g-riesz basis / g-riesz frame / sub-g-frame property / g-linearly independent

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郭训香. g-框架的一些新性质. 数学学报, 2014, 57(5): 881-892 https://doi.org/10.12386/A2014sxxb0082
Xun Xiang GUO. Some New Properties of g-Frames. Acta Mathematica Sinica, Chinese Series, 2014, 57(5): 881-892 https://doi.org/10.12386/A2014sxxb0082

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