Hilbert空间中连续广义框架的分解

On decompositions of continuous generalized frames in Hilbert spaces

利用连续广义预框架算子,刻画了连续广义框架、Parseval连续广义框架、连续广义Riesz基及连续广义标准正交基;通过已建立的刻画结果及有界算子的分解,得到了连续广义框架可以表示特殊的或者更简单的连续广义框架的线性组合,比如连续广义标准正交基、连续广义Riesz-基、Parseval连续广义框架。

This paper establishes the characterization of continuous generalized frames, Parseval continuous g-frames, continuous gen eralized Riesz bases and continuous generalized orthonormal bases in term of the continuous generalized preframe operator. Using the established characterization results and decompositions of bounded operators, the representation of continuous generalized frames in term of linear combinations of simpler ones such as continuous generalized orthonormal bases, continuous generalized Riesz bases and Parseval continuous generalized frames is studied.