Hilbert K-子模上框架的(强)可补性

兰州理工大学学报 ›› 2021, Vol. 47 ›› Issue (1): 150-154.

Hilbert K-子模上框架的(强)可补性

董芳芳, 裴瑞昌

天水师范学院数学与统计学院, 甘肃天水 741001

收稿日期:2019-11-18 出版日期:2021-02-28 发布日期:2021-03-11
作者简介:董芳芳(1981-),女,甘肃天水人,硕士,讲师.
基金资助:
国家自然科学基金(11661070)

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

DONG Fang-fang, PEI Rui-chang

College of Mathematical and Statistics, Tianshui Normal University, Tianshui 741001, China

Received:2019-11-18 Online:2021-02-28 Published:2021-03-11

摘要/Abstract

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.

关键词: Hilbert K-子模, Hilbert基, 正交投影, (强)可补, 正交补

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.

Key words: Hilbert K-submodule, Hilbert base, orthogonal projection, (strong) complement, orthogonal complement

中图分类号:

O177.1

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): 150-154.

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): 150-154.