K-g-框架及其对偶

戴春年, 冷劲松, 何苗

数学学报 ›› 2021, Vol. 64 ›› Issue (2) : 243-254.

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PDF(476 KB)
数学学报 ›› 2021, Vol. 64 ›› Issue (2) : 243-254. DOI: 10.12386/A2021sxxb0021
论文

K-g-框架及其对偶

    戴春年, 冷劲松, 何苗
作者信息 +

K-g-frames and Their Duality

    Chun Nian DAI, Jin Song LENG, Miao HE
Author information +
文章历史 +

摘要

本文主要探讨K-g-框架及其对偶.首先讨论K-g-框架和g-框架的关系,然后给出一些充分条件,使得在此条件下K-g-框架与g-Bessel序列经过有界线性算子或非零复有界序列作用后的和仍然是K-g-框架.此外,又给出K-g-框架求和的两种特殊形式.最后,研究K-g-框架在闭子空间RK)上的对偶,以及利用近似对偶构建K-g-框架的方法.

Abstract

We mainly discuss K-g-frames and its duality. First, we explore the relationship between K-g-frames and g-frames. Then, we give some sufficient conditions under which the sum of K-g-frames and g-Bessel sequences with bounded linear operator or nonzero complex bounded sequence is still K-g-frames. In addition, we also give two special forms about the sum of K-g-frames. Finally, we research the duality of K-g-frames in closed subspace R(K), and the ways of constructing the K-g-frames by using the approximate duality.

关键词

K-g-框架 / / 对偶K-g-Bessel序列 / 近似对偶K-g-Bessel序列

Key words

K-g-frames / sum / dual K-g-Bessel sequence / approximate dual K-g-Bessel sequence

引用本文

导出引用
戴春年, 冷劲松, 何苗. K-g-框架及其对偶. 数学学报, 2021, 64(2): 243-254 https://doi.org/10.12386/A2021sxxb0021
Chun Nian DAI, Jin Song LENG, Miao HE. K-g-frames and Their Duality. Acta Mathematica Sinica, Chinese Series, 2021, 64(2): 243-254 https://doi.org/10.12386/A2021sxxb0021

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基金

成都电子科技大学理科实力提升与拓展计划项目(Y0301902610100202)
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