连续框架的等价刻画及Riesz型框架的新结果

Equivalent Characterizations of Continuous Frames and New Results of Riesz-Type Frames

首先通过引入伪逆算子的相关结论,给出了连续框架的等价刻画.然后讨论连续框架的对偶框架,给出了预框架算子的伪逆算子的详细刻画.最后,利用Gabardo等人关于Riesz型框架的结果,得到了Riesz型框架的新结果.

Two equivalent characterizations of continuous frame are given through introducing the correlated conclusions of pseudo-inverse operator. The duals of continuous frames are discussed. An explicit characterization for the pseudo-inverse of the pre-frame operator is presented. Finally, some new results for Riesz-type frames are also obtained by using the existing result of Gabardo et al. on Riesz-type frame.