K-g-框架及其对偶

K-g-frames and Their Duality

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R(K)上的对偶,以及利用近似对偶构建K-g-框架的方法.

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.