Hilbert K-子模上框架的(强)可补性  

The(strong)complements of frames in Hilbert K-submodules

作　　者：董芳芳[1] 裴瑞昌[1] DONG Fang-fang;PEI Rui-chang(College of Mathematical and Statistics, Tianshui Normal University, Tianshui 741001, China)

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001

出　　处：《兰州理工大学学报》2021年第1期150-154,共5页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11661070)。

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.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.

关 键 词：Hilbert K-子模 Hilbert基 正交投影 (强)可补 正交补 

分 类 号：O177.1[理学—基础数学]