Banach空间中Riesz基的稳定性

Stability of Riesz Bases on Banach Space

利用泛函分析中的线性同胚及有界线性算子理论,研究Banach空间中Riesz基的稳定性问题.即当{xn}为Banach空间X的Riesz基时,设T为X→X的线性同胚的有界线性算子,若存在M≥0,A>0,β≥0,使A>(βA+M)‖T‖,且{yn}满足对任意c={cn}∈l2,有‖∑cnyn‖≤β‖∑cnxn‖+M‖c‖,则{xn+T(yn)}也为X的Riesz基.

It reseaches stability of Riesz base on Banach space through linear homeomorphism of functional analysis and bounded linear operator theory.Let {x_n} be a Riesz bases of Banach space X and T:X→X be a linear homeomorphism and a bounded linear operator,if there exist M≥0,A>0,β≥0,that enableA>(βA+M)‖T‖,and {y_n} satisfies‖∑c_ny_n‖≤β‖∑c_nx_n‖+M‖c‖for any c={c_n}∈l^2,{x_n+T(y_n)} is also a Riesz base of X.