Banach空间上有界可逆线性变换逆变换的结构 |
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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 |
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作者姓名: | 陈全园 周永正 |
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作者单位: | 景德镇陶瓷学院,江西,景德镇,333001 |
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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.
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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: | 2002-08-23 |
The Structure of Inverse Transformation for Linear Invertible Bounded Transformation on Banach Space |
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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. |
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Keywords: | linear invertible transformation invariant subspace of transformation polinominal in A local polinominal in A |
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