Hilbert空间连续K-框架的冗余与扰动性

Excess and perturbation of continuous K- frames in Hilbert spaces

基于连续K-框架的定义,给出了Hilbert空间连续K-框架的两个等价刻画.在连续K-框架中挖去部分元素还构成连续K-框架的两个充分条件和不构成连续K-框架的一个充分条件,利用合成算子和两个连续Bessel映射的有界线性算子SF,G去刻画连续K-框架.最后讨论Hilbert空间连续K-框架的扰动.

Based on the definition of the continuous K - frames, we propose two kinds of equivalent characterizations for continuous K- frames. We also give two sufficient conditions for the remainder of a continuous K- frame after deleting some elements to be a continuous K -frame and a sufficient con- dition for the remainder to be not a continuous K- frame. We characterize the continuous K- frames by the synthesis operator and a bounder operator SF,G associated with two continuous Bessel mappings. Finally, we discuss the perturbation of continuous K - frames in Hilbert spaces.