Banach空间上的逼近对偶g-框架

Approximate Duality of Banach Frames in Banach Spaces

本文提出了可分且自反的Banach空间X中的逼近对偶g-框架的定义,得到了Banach空间上逼近对偶的一些性质与Banach空间上逼近对偶框架的一些新的结果,并把它们推广到了融和框架甚至g-框架.证明了Banach空间上逼近对偶框架与框架和原子分解有着紧密的联系,相应的结论也推广到了g-框架上.最后,得到了Banach空间逼近对偶g-框架在扰动下的稳定性.

A definition of the approximate dual g-frames in the separable and self-adjoint Banach spaces is given. Some properties of approximate dual and new results of approximate duality of frames in Banach spaces are obtained. The results in approximate duality of frames are also generalize to fusion frames and even to g-frames. It is proved that the approximate duality of frames in Banach spaces have a strong connection with Banach frames and atomic decomposition. The corresponding results are generalized to g-frames. At last, it is shown that the approximate duality of g-frames are stable under the perturbation.