Banach空间中q-框架的近关系及强稳定性

The Close Relations and Strong Stability on the q-frames in Banach Spaces

根据Hilbert空间中框架之间的近关系,在Banach空间中引入了q-框架之间的近关系以及q-框架关于扰动的强稳定性的新概念,并且得出了判断q-框架强稳定性的一个充分条件,丰富了Paley-Wiener定理的扰动结果,并且满足所提出的强稳定性。

There were a lot of frame theories in Hilbert spaces,scholars extended them to Banach spaces and obtained some significant conclusions.According to the close relations between frames in Hilbert spaces,we,in Banach spaces,introduced the new concepts of close relations between q-frames and strong stability of q-frames about disturbance,and obtained a sufficient condition of determining the strong stability of q-frames,enriching the disturbance results of Paley-Wiener theorem and satisfying the strong stability proposed in the paper.