Hilbert空间连续K-框架的若干研究

Several studies of continuous K-frame in Hilbert spaces

在Hilbert空间引入连续K-框架的概念,给出连续K-框架的多种等价刻画,同时给出连续K-框架的交错对偶对所涉及的两个序列可互换的一个充分条件及一种具体的构造连续K-框架交错对偶对的方法.最后给出两种不同的方法去构造新的连续K-框架.

In the paper,we introduced the concept of continuous K-frame in Hilbert spaces,gave several kinds of equivalent characterizations for continuous K-frames.We also gave a sufficient condition for the two sequences involving in an alternate dual pair of continuous K-frames to be commutable,and a concrete method to construct an alternate dual pair of continuous K-frames.Finally we presented two different methods to construct new continuous K-frames.