K-frames and its K-dual Bessel sequences(K-框架及其K-对偶Bessel序列)

Abstract

K-frames and its K-dual Bessel sequences are discussed. The sufficient and necessary condition for a Bessel sequence to be a K-frame is obtained. Then, we research the duality of K-frames in closed subspace R(K), and the ways of constructing the K-frames by using approximate K-dual. In addition, we give the sufficient and necessary condition for two K-frames to be approximate K-dual, and give a simple method to obtain approximate K-dual.(研究了K-框架及其K-对偶Bessel序列。首先，给出了Bessel序列为K-框架的充要条件，在闭子空间R（K）上借助逼近K-对偶，研究了构造K-框架及其对偶的方法。其次，给出了两个K-框架是逼近K-对偶的充要条件，得到了构造逼近K-对偶的简单方法。最后，基于K-对偶Bessel序列，在R（K）上构造了可与K-框架交换位置的Bessel序列。)

Keywords

• hilbert space(hilbert空间)
• k-frames(k-框架)
• bessel sequence(bessel序列)
• k-dual bessel sequence(k-对偶bessel序列)
• approximate k-dual frames(逼近k-对偶)
• orthogonal projection operator(正交投影算子)