Hilbert空间中的K-框架

丁明玲, 肖祥春, 朱玉灿

数学学报 ›› 2014, Vol. 57 ›› Issue (6) : 1089-1100.

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数学学报 ›› 2014, Vol. 57 ›› Issue (6) : 1089-1100. DOI: 10.12386/A2014sxxb0100
论文

Hilbert空间中的K-框架

    丁明玲1, 肖祥春2
作者信息 +

K-Frames in Hilbert Spaces

    Ming Ling DING1, Xiang Chun XIAO2
Author information +
文章历史 +

摘要

K-框架是框架理论的一种推广.K-框架可以用于重构Hilbert空间中有界线性算子值域内的元素.本文首先研究了K-框架与框架理论的关系,得到了紧K-框架成为框架当且仅当有界线性算子K是满的,给出了有界线性算子K具有闭值域的K-框架的一个充要条件.并利用有界线性算子K和合成算子构造K-框架,讨论在一定扰动条件下K-框架的稳定性.

Abstract

K-frames, which are a generalization of frames, allow us in a stable way, to reconstruct elements from the range of a linear and bounded operator in a Hilbert space.In this paper, we first make a discussion on relations between K-frames and frames.We obtain that a tight K-frame turns to be a frame if and only if the linear and bounded operator K is surjective, and then give a necessary and sufficient condition for a K-frame with closed range operator K.We also study the constructions of K-frames under some conditions.Finally we study the stabilities of K-frames under small perturbations.

关键词

K-框架 / 框架 / 局部框架 / 稳定性

Key words

K-frame / frame / local frame / stability

引用本文

导出引用
丁明玲, 肖祥春, 朱玉灿. Hilbert空间中的K-框架. 数学学报, 2014, 57(6): 1089-1100 https://doi.org/10.12386/A2014sxxb0100
Ming Ling DING, Xiang Chun XIAO, Yu Can ZHU. K-Frames in Hilbert Spaces. Acta Mathematica Sinica, Chinese Series, 2014, 57(6): 1089-1100 https://doi.org/10.12386/A2014sxxb0100

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基金

福建省自然科学基金(2012J01005,2014J01007);福州大学科技发展基金(2012-XQ-29)资助项目

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