酉系统中的受控K-融合框架生成子

Controlled K-fusion Frame Generators for Unitary Systems

本文引入了酉系统中的(C,C’)-受控融合框架生成子和(C,C’)-受控K-融合框架生成子的概念,它们都是框架的推广.研究了酉系统中的(C,C’)-受控融合框架生成子和融合框架生成子之间的关系,并给出了(C,C’)-受控K-融合框架生成子的一些刻画.此外,探讨了Hilbert空间H的一个闭子空间成为(C,C’)-受控融合框架生成子以及(C,C’)-受控K-融合框架生成子的条件.

In this paper,we introduce the concepts of the(C,C')-controlled fusion frame generators and the(C,C')-controlled K-fusion frame generators for unitary systems,which are a generalization of frames.We study the relationship between(C,C')-controlled fusion frame generators and fusion frame generators.Also,we display some characterizations of the controlled K-fusion frame generators.Moreover,the condition for a closed subspace of Hilbert space H to be a(C,C')-controlled fusion frame generator and a(C,C')-controlled K-fusion frame generator is discussed.