【摘要】 运用算子论的方法,讨论了Banach空间中Banach框架的扰动性问题.给定X关于Xd的Banach框架（{g_i}_i∈Ν,S）和有界算子T:X_d→X,探讨其在算子的作用下,得到新序列{φ_i}_i∈ΝX^*使得({φ_i}_i∈Ν,T)为X关于X_d的Banach框架;给定X关于X_d的Banach框架({g_i}_i∈Ν,S)和序列{φ_i}_i∈ΝX^*,讨论其在序列的扰动下,存在有界算子U:X_d→X使得({φ_i}_i∈Ν,U)为X关于X_d的Banach框架.同时表明已知结论是新结论的推广.更多还原

【Abstract】 The problem of perturbation of Banach frame in Banach space is discussed by using the operator theory. First,given the Banach frame( { g_i}_i∈Ν,S) for X with respect to Xdand the bounded operator T: X_d→X,it is discussed under the action of the operator to obtain a new sequence { φi}_i∈Ν X^* that makes( {φ_i}_i∈Ν,T) be a Banach frame for X with respect to X_d; secondly: Given the Banach frame({ g_i}_i∈Ν,S) for Xwith respect to Xdand the sequence{φ_i}_i∈ΝX^*,Under the perturbation of the sequence,there is a bounded operator making it for the Banach frame. At the same time,the article shows that the known conclusion is generalized by the new conclusion.更多还原