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The Spectrum of Linear Operators on Quotient Indecomposable Banach Spaces
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作者 苏维钢 《Northeastern Mathematical Journal》 CSCD 2006年第2期233-240,共8页
This paper discusses the special properties of the spectrum of linear operators (in particular, bounded linear operators) on quotient indecomposable Banach spaces; shows that in such spaces generators of C0-groups a... This paper discusses the special properties of the spectrum of linear operators (in particular, bounded linear operators) on quotient indecomposable Banach spaces; shows that in such spaces generators of C0-groups are always bounded linear operators, and that generators of C0-semigroups satisfy the spectral mapping theorem; and gives an example to show that the generators of C0-semigroups in quotient indecomposable spaces are not necessarily bounded. 展开更多
关键词 banach space quotient indecomposable spectrum generator
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Maps Preserving Peripheral Spectrum of Generalized Jordan Products of Operators 被引量:1
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作者 Wen ZHANG Jin Chuan HOU Xiao Fei QI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第6期953-972,共20页
Let X1 and X2 be complex Banach spaces with dimension at least three, A1 and A2 be standard operator algebras on X1 and X2, respectively. For k ≥ 2, let (i1, i2, . . . , im) be a finite sequence such that {i1, i2, ... Let X1 and X2 be complex Banach spaces with dimension at least three, A1 and A2 be standard operator algebras on X1 and X2, respectively. For k ≥ 2, let (i1, i2, . . . , im) be a finite sequence such that {i1, i2, . . . , im} = {1, 2, . . . , k} and assume that at least one of the terms in (i1, . . . , im) appears exactly once. Define the generalized Jordan productT1 o T2 o··· o Tk = Ti1Ti2··· Tim + Tim··· Ti2Ti1 on elements in Ai. This includes the usual Jordan product A1A2 + A2A1, and the Jordan triple A1A2A3 + A3A2A1. Let Φ : A1 → A2 be a map with range containing all operators of rank at most three. It is shown that Φ satisfies that σπ(Φ(A1) o··· o Φ(Ak)) = σπ(A1 o··· o Ak) for all A1, . . . , Ak, where σπ(A) stands for the peripheral spectrum of A, if and only if Φ is a Jordan isomorphism multiplied by an m-th root of unity. 展开更多
关键词 Peripheral spectrum generalized Jordan products banach spaces standard operatoralgebras
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Banach空间结构理论的重大进展 ──关于Gowers-Maurey系列成果 被引量:30
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作者 钟怀杰 《数学进展》 CSCD 北大核心 2000年第1期1-18,共18页
最近,Gowers W. T.和 Maurey B.构造出第一例遗传不可分解空间,否定地解决了无条件基序列问题,由此导致了 Banach空间结构理论研究中系列问题的解决.本综述介绍这一新动向,反映G-M系列成果.全文分为... 最近,Gowers W. T.和 Maurey B.构造出第一例遗传不可分解空间,否定地解决了无条件基序列问题,由此导致了 Banach空间结构理论研究中系列问题的解决.本综述介绍这一新动向,反映G-M系列成果.全文分为七个部分:1.历史回顾与问题沿革;2. G-M空间XG1及其遗传不可分解性质;3.关于空间 XG1上的算子构成; 4.关于共轭空间 XG1;5.关于 G-M的系列成果; 6. G-M型空间构造的新视角探讨;7.OPen问题总汇. 展开更多
关键词 G-M型空间 无条件基序列 巴拿赫空间 算子
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关于G-M成果研究的若干新动态Ⅰ——G-M型空间的若干品种 被引量:3
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作者 钟怀杰 程立新 《应用泛函分析学报》 CSCD 2002年第1期60-68,共9页
结合自己的工作 ,对 Gowers-Maurey系列成果获 Fields奖以来的研究的新动态作一综述 .本文是上篇 ,主要讨论含遗传不可分解空间在内的 G-M型空间的若干品种 .
关键词 banach空间 G-M型空间 遗传不可分解空间 遗传不能合成空间 商不能合成空间
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