Banach空间中Banach框架的扰动性  

Perturbation of Banach Frame in Banach Space

作　　者：侯美琴[1] 姚喜妍[2] HOU Mei-qin YAO Xi-yan(School of Mathematics and Computer Science, Shanxi Normal University, Linfen Shanxi 041000, China Department of Applied Mathematics, Yuncheng University, Yuncheng Shanxi 044000, China)

机构地区：[1]山西师范大学数学与计算机科学学院,山西临汾041000 [2]运城学院应用数学系,山西运城044000

出　　处：《淮阴师范学院学报（自然科学版）》2017年第2期95-99,共5页Journal of Huaiyin Teachers College;Natural Science Edition

基　　金：山西省自然科学基金资助项目(20130111003-1);山西省高校重点学科建设专项基金项目(20131010)

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.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.

关 键 词：算子 BANACH框架 扰动性 

分 类 号：O177.1[理学—数学]