| Hilbert K_子模上广义框架的（强）可补性 |
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| 引用本文： | 董芳芳.Hilbert K_子模上广义框架的（强）可补性[J].福州大学学报(自然科学版),2021,49(4):447-450. |
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| 作者姓名： | 董芳芳 |
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| 作者单位： | 甘肃省天水师范学院数学与统计学院 |
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| 摘 要： | 引入Hilbert K-子模上广义框架的广义框架变换和正交投影,研究二者的关系.重新定义Hilbert K-模上的广义Hilbert基、(强)可补、直和的内积等概念,从正交投影的角度得到了Hilbert K-子模上两广义框架(强)可补的充要条件,并进行了推广.
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| 关 键 词： | Hilbert K-子模 广义Hilbert 基 正交投影 （强）可补 正交补 |
| 收稿时间： | 2020/3/24 0:00:00 |
| 修稿时间： | 2020/6/17 0:00:00 |
The (Strong) Complement of Generalized Frames in Hilbert K-Submodules |
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| Institution: | College of Mathematical and Statistics, Tianshui Normal University |
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| Abstract: | In this paper, the concepts of generalized frame transform and orthogonal projection in Hilbert K-submodules are introduced and the relationship between them is studied, the generalized Hilbert base, the (strong) complement of generalized frames and the inner product of straight sum in Hilbert K-modules are redefined, Finally, the necessary and sufficient conditions of (strong) complements of generalized frames in Hilbert K-submodules are obtained and generalized from the aspect of orthogonal projection. |
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| Keywords: | Hilbert K-submodule generalized Hilbert base orthogonal projection (strong) complement orthogonal complement |
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