| Nonlinear Preserver Problems on B（H） |
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| 作者姓名： | Jian Lian CUI |
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| 作者单位： | Department of Mathematical Science, University of Tsinghua, Beijing 100084, P. R. China |
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| 基金项目： | Supported by National Natural Science Foundation of China （Grant Nos. 10871111, 10501029） and the Specialized Research Fund for Doctoral Program of Higher Education （Grant No. 200800030059） |
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| 摘 要： |
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| 关 键 词： | 线性保持问题 Banach代数 非线性连续 空间尺寸 希尔伯特 二元关系 偏序集 算子集 |
Nonlinear preserver problems on <Emphasis Type="Italic">B</Emphasis>(<Emphasis Type="Italic">H</Emphasis>) |
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| Jian Lian,CUI.Nonlinear preserver problems on B(H)[J].Acta Mathematica Sinica,2011,27(1):193-202. |
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| Authors: | Jian Lian Cui |
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| Institution: | 1.Department of Mathematical Science,University of Tsinghua,Beijing,P. R. China |
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| Abstract: | Let H be a complex Hilbert space of dimension greater than 2, and B(H) denote the Banach algebra of all bounded linear operators on H. For A, B ∈ B(H), define the binary relation A ≤* B by A*A = A*B and AA* = AB*. Then (B(H), “≤*”) is a partially ordered set and the relation “≤*” is called the star order on B(H). Denote by Bs(H) the set of all self-adjoint operators in B(H). In this paper, we first characterize nonlinear continuous bijective maps on B
s
(H) which preserve the star order in both directions. We characterize also additive maps (or linear maps) on B(H) (or nest algebras) which are multiplicative at some invertible operator. |
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| Keywords: | Star order fundamental operator algebras nest algebras preserver problems |
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