| Hilbert K-子模上框架的(强)可补性 |
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| 引用本文： | 董芳芳,裴瑞昌.Hilbert K-子模上框架的(强)可补性[J].兰州理工大学学报,2021,47(1):150. |
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| 作者姓名： | 董芳芳 裴瑞昌 |
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| 作者单位： | 天水师范学院数学与统计学院, 甘肃天水 741001;天水师范学院数学与统计学院, 甘肃天水 741001 |
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| 基金项目： | 国家自然科学基金(11661070) |
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| 摘 要： | 引入了Hilbert K-子模上框架的框架变换和正交投影,重新定义了Hilbert K-模上的Hilbert 基,(强)可补,直和的内积等概念,通过探讨框架变换和正交投影之间的关系,研究了Hilbert K-子模上框架的(强)可补性,得到了一些重要结论,并加以推广.
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| 关 键 词： | HilbertK-子模 Hilbert基 正交投影 (强)可补 正交补 |
| 收稿时间： | 2019-11-18 |
The (strong) complements of frames in Hilbert K-submodules |
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| DONG Fang-fang,PEI Rui-chang.The (strong) complements of frames in Hilbert K-submodules[J].Journal of Lanzhou University of Technology,2021,47(1):150. |
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| Authors: | DONG Fang-fang PEI Rui-chang |
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| Institution: | College of Mathematical and Statistics, Tianshui Normal University, Tianshui 741001, China |
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| Abstract: | The concepts of frame transform and orthogonal projection in Hilbert K-submodulesare are introduced in this paper. The Hilbert base, the (strong) complement of frames and the inner product of straight sum in Hilbert K-modules are redefined hereby. The (strong) complements of frames in Hilbert K-submodules are mainly studied from the aspect of orthogonal projection by the relationship between the frame transform and the orthogonal projection. Finally, some important results coming from the researches are obtained and generalized. |
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| Keywords: | Hilbert K-submodule Hilbert base orthogonal projection (strong) complement orthogonal complement |
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