线性算子L的性质及其应用

Properties and Applications of Linear Operator L

利用泛函分析中的算子理论讨论了Hilbert空间中框架扰动的稳定性结果,并且改进了已有的相关结果:线性算子的条件是可逆的减弱为是满的,证明了对于Riesz基也有类似的扰动性结果。进一步研究了该线性算子的性质,并且把它应用到研究框架的交错对偶中。

The stability of frames under perturbation in Hilbert spaces was discussed by using the operator theory in functional analysis, and some new results were obtained. It is proved that the invertible requirement for a linear operator can be weakened to be a subjective one, and similar results also be obtained for Riesz basis under perturbation. The properties of the linear operator are further studied, which are applied into the alternate dual frames.