| Banach空间上有界可逆线性变换逆变换的结构 |
| |
| 引用本文： | 陈全园,周永正.Banach空间上有界可逆线性变换逆变换的结构[J].大学数学,2003,19(5):79-81. |
| |
| 作者姓名： | 陈全园 周永正 |
| |
| 作者单位： | 景德镇陶瓷学院,江西,景德镇,333001 |
| |
| 摘 要： | Fillmore在1]中得到一个定理:设A,T是Banach空间X上的线性变换,A有界,若Lat(A) Lat(T)且AT=TA,则T是A的多项式.在本文里,以此作为引理,讨论了Banach空间上可逆线性变换A在什么情况下,A-1可表示为A的多项式.本文最主要的结论是定理3.4:设X是Banach空间,A是X上的有界线性变换,且可逆,则A-1是A的多项式当且仅当A-1是A的局部多项式.
|
| 关 键 词： | 可逆线性变换 不变子空间 A的多项式 A的局部多项式 |
| 文章编号： | 1672-1454(2003)05-0079-03 |
| 修稿时间： | 2002年8月23日 |
The Structure of Inverse Transformation for Linear Invertible Bounded Transformation on Banach Space |
| |
| Abstract: | It was shown by Fillmore in 1] that linear transformations A and T on a Banach space, with A bounded. If Lat(A)Lat(T) under what conditions and T commutes with A, then T is a polynominal in A. In this paper, we discuss the problem: discuss the problem that A-1 is a polynominal in A when A is a linear invertible transformation on a Banach space. The main result is that if A is a linear transformation on a Banach space with A bounded and invertible, then A-1 is a polynominal in A if and only if A-1 is locally a polynominal in A. |
| |
| Keywords: | linear invertible transformation invariant subspace of transformation polinominal in A local polinominal in A |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
